diff --git a/Assignment-2.ipynb b/Assignment-2.ipynb new file mode 100644 index 0000000..9fd4bc0 --- /dev/null +++ b/Assignment-2.ipynb @@ -0,0 +1,566 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f57181a5-9001-42b0-a5cb-3549c8fb9300", + "metadata": {}, + "source": [ + "**Question 1**
\n", + "given,
$\\theta\\to N(5,9)$
$x \\to N(\\theta,4)$

\n" + ] + }, + { + "cell_type": "markdown", + "id": "a9161e4b-1b8a-4da0-9c2e-5c81a1b247d9", + "metadata": {}, + "source": [ + "**1.1)** $P(\\theta|X)=\\frac{P(X|\\theta).P(\\theta)}{P(X)}$

\n", + "now X=6
$P(\\theta|6)=\\frac{P(6|\\theta).P(\\theta)}{P(6)}$
\n", + "where, $P(\\theta|6)$ is posterior.
\n", + "$P(\\theta)=\\frac{1}{3\\sqrt{2\\pi}}e^{-\\frac{1}{2}.(\\frac{\\theta-5}{3})^{2}}$
\n", + "$P(6|\\theta)=\\frac{1}{2\\sqrt{2\\pi}}e^{-\\frac{1}{2}.(\\frac{6-\\theta}{2})^{2}}$
\n", + "$P(6)=\\int_{-\\infty}^{\\infty}\\frac{1}{12\\pi}e^{-\\frac{1}{2}.((\\frac{6-\\theta}{2})^{2}+(\\frac{\\theta-5}{3})^{2})}$

\n", + "on solving the integral we get,
\n", + "$P(6).12\\pi=\\dfrac{3{\\cdot}2^\\frac{3}{2}\\mathrm{e}^{-\\frac{1}{26}}\\sqrt{{\\pi}}}{\\sqrt{13}}$
\n", + "after substituting and simplyfying we get
\n", + "$P(\\theta|6)=\\frac{e^{-(\\frac{13\\theta^2-148\\theta+424}{72})}}{\\dfrac{3{\\cdot}2^\\frac{3}{2}\\mathrm{e}^{-\\frac{1}{26}}\\sqrt{{\\pi}}}{\\sqrt{13}}}$ = $\\frac{1}{\\sqrt{\\frac{36}{13}.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(\\theta-\\frac{74}{13})^{2}}{\\frac{36}{13}})}$
\n", + "$P(\\theta|6) \\to N(\\frac{74}{13},\\frac{36}{13})$
" + ] + }, + { + "cell_type": "markdown", + "id": "39465689-df5a-4eb3-a10a-67a1d015ba6e", + "metadata": {}, + "source": [ + "**1.2)**
\n", + "Given,
\n", + "Noise~N($\\theta$,4)
\n", + "prior P($\\theta$) $\\to$ N(5,9)\n", + "$\\mu_{prior}=5$,$\\sigma^{2}_{prior}=9$
\n", + "using normal-normal bayesian updating,
\n", + "$a=\\frac{1}{\\sigma^{2}_{prior}},b=\\frac{n}{\\sigma^{2}_{likelihood}}=\\frac{n}{4}$
\n", + "therefore,
\n", + "$\\mu_{post}=\\frac{20+9n\\bar{x}}{9n+4}$\n", + "$\\sigma^{2}_{post}=\\frac{36}{9n+4}$
" + ] + }, + { + "cell_type": "markdown", + "id": "29bb8da2-64c1-49c0-99af-6087b091bb96", + "metadata": {}, + "source": [ + "**1.3)** As the number of samples are increased n$\\to\\infty$ the variance tends to 0 this shows that more samples occupy the gaps in the cluster of data making it more concentrated. And as variance tends to zero shows its convergence hence we can calculate $\\theta$ with more certainity.
\n", + "
\n", + "Also, as $n \\to \\infty$ we can observe that the posterior mean tends to the sample mean $\\bar{x}$ as its weight increases.
" + ] + }, + { + "cell_type": "markdown", + "id": "6d622931-9fe1-4ca7-acda-c35bdf71863f", + "metadata": {}, + "source": [ + "**1.4)** Given,
\n", + "True IQ(Y) = N(100,152) $\\to$ prior
\n", + "True(Y) - Test(X) = N(0,102)
\n", + "if Test(X=x) then, Y|X=x ~ N(x,102) $\\to$ likelihood
\n", + "now to find posterior we can use bayes' inference
\n", + "posterior = (likelihood*prior)/evidence

\n", + "**1.4.1)** x=80;
\n", + "posterior = $\\frac{\\frac{1}{\\sqrt{102.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-80)^2}{102})}.\\frac{1}{\\sqrt{152.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-100)^2}{152})}}{\\int_{-\\infty}^{\\infty}\\frac{1}{\\sqrt{102.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-80)^2}{102})}.\\frac{1}{\\sqrt{152.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-100)^2}{152})}}$

\n", + "E(posterior) = $\\int_{-\\infty}^{\\infty}y.\\frac{\\frac{1}{\\sqrt{102.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-80)^2}{102})}.\\frac{1}{\\sqrt{152.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-100)^2}{152})}}{\\int_{-\\infty}^{\\infty}\\frac{1}{\\sqrt{102.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-80)^2}{102})}.\\frac{1}{\\sqrt{152.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-100)^2}{152})}}$
\n", + "on solving the integrals we get,
\n", + "E(posterior)= $\\frac{44720}{4.127}$ = **88.03**

\n", + "**1.4.2)** x=150;
\n", + "posterior = $\\frac{\\frac{1}{\\sqrt{102.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-150)^2}{102})}.\\frac{1}{\\sqrt{152.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-100)^2}{152})}}{\\int_{-\\infty}^{\\infty}\\frac{1}{\\sqrt{102.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-150)^2}{102})}.\\frac{1}{\\sqrt{152.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-100)^2}{152})}}$

\n", + "E(posterior) = $\\int_{-\\infty}^{\\infty}y.\\frac{\\frac{1}{\\sqrt{102.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-150)^2}{102})}.\\frac{1}{\\sqrt{152.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-100)^2}{152})}}{\\int_{-\\infty}^{\\infty}\\frac{1}{\\sqrt{102.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-150)^2}{102})}.\\frac{1}{\\sqrt{152.2\\pi}}e^{-\\frac{1}{2}.(\\frac{(y-100)^2}{152})}}$
\n", + "on solving the integrals we get,(or using normal-normal bayesian updating)
\n", + "E(posterior)= $\\frac{66000}{4.127}$ = **129.92**

" + ] + }, + { + "cell_type": "markdown", + "id": "ed74e7e7-488e-492e-b774-5f76ff2b6d88", + "metadata": {}, + "source": [ + "**Question 2:**" + ] + }, + { + "cell_type": "markdown", + "id": "dbba4d75-cf4c-439e-ab9c-055d2346c2b7", + "metadata": {}, + "source": [ + "N($\\mu,\\sigma^{2}$)
\n", + "$f(x)=\\frac{1}{\\sigma\\sqrt{2\\pi}}e^{\\frac{-(x-\\mu)^2}{2\\sigma^2}}$
\n", + "suppose we have n samples,\n", + "$x_1,x_2,x_3....,x_n$
\n", + "liikelihood function,
\n", + "$L(\\theta)=f(x_1).f(x_2).f(x_3)....f(x_n)=\\frac{1}{(2\\pi)^{n/2}(\\sigma)^n}e^{\\frac{-1}{2\\sigma^2}[(x_1-\\mu)^{2}+(x_2-\\mu)^{2}+....(x_n-\\mu)^{2}]}$\n", + "
\n", + "now to maximize likelihood wrt $\\mu$ and $\\sigma$,
\n", + "to make calculations simpler lets take log-likelihood,
\n", + "$log(L(\\theta))=-\\frac{n}{2}log(2\\pi)-nlog(\\sigma)-\\frac{1}{2\\sigma^2}[(x_1-\\mu)^{2}+(x_2-\\mu)^{2}+....(x_n-\\mu)^{2}]$

\n", + "$\\frac{d(log(L(\\theta)))}{d\\mu}=0$

\n", + "$\\mu=\\frac{\\sum_{i=1}^{n}x_i}{n}$

\n", + "$\\frac{d(log(L(\\theta)))}{d\\sigma}=0$

\n", + "$-\\frac{n}{\\sigma}+\\frac{1}{\\sigma^3}(\\sum_{1=n}^n(x_i)^2+n\\mu^2-2\\mu\\sum_{i=1}^nx_i)=0$
\n", + "$\\sigma=\\frac{1}{n}\\sum_{i=1}^n(x_i)^2+\\mu^2-2\\mu\\sum_{i=1}^n\\frac{x_i}{n}$

\n", + "$\\sigma^2=\\frac{\\sum(x_i-\\mu)^2}{n}$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "ab96029a-2448-4076-8fed-4606b48c2c64", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MLE Estimates:\n", + "mu = 6.977867773182721\n", + "sigma = 2.9495817597206218\n", + "\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "from scipy.optimize import minimize\n", + "import matplotlib.pyplot as plt\n", + "from scipy.stats import norm\n", + "\n", + "true_mu = 7\n", + "true_sigma = 3\n", + "data = np.random.normal(true_mu, true_sigma, 1000)\n", + "\n", + "def neg_log_likelihood(params, data):\n", + " mu, sigma = params[0], params[1]\n", + " if sigma <= 0: \n", + " return np.inf\n", + " n = len(data)\n", + " ll = -0.5 * n * np.log(2 * np.pi) - n * np.log(sigma) - (1 / (2 * sigma ** 2)) * np.sum((data - mu) ** 2)\n", + " return -ll \n", + "\n", + "guess = [0, 1]\n", + "result = minimize(neg_log_likelihood, guess, args=(data,), bounds=[(None, None), (1e-6, None)])\n", + "mle_mu, mle_sigma = result.x\n", + "\n", + "print(f\"MLE Estimates:\\nmu = {mle_mu}\\nsigma = {mle_sigma}\\n\")\n", + "\n", + "x = np.linspace(min(data),max(data),1000)\n", + "original_pmf = norm.pdf(x,true_mu,true_sigma)\n", + "estimated_pmf = norm.pdf(x,mle_mu,mle_sigma)\n", + "plt.plot(x,original_pmf,label='Original Distribution',alpha=0.5)\n", + "plt.plot(x,estimated_pmf,label='ML Estimated distribution',alpha=0.5)\n", + "plt.xlabel('x') \n", + "plt.ylabel('P(X=x)') \n", + "plt.title('Maximum Likelihood Estimate') \n", + "plt.legend() \n", + "plt.grid(True) \n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "656c8f12-bd54-4dc5-b2e6-16d49d5b685c", + "metadata": {}, + "source": [ + "
**Question 3:**
\n", + "In a logistic regression model,
\n", + "X is the input vector,
\n", + "Y is the label vector and
\n", + "w is the parameter vector.
\n", + "and the probability of ith label $y_i$ given the input $x_i$ and the parameter w
can be modeled by using sigmoid function $\\sigma(z)=\\frac{1}{1+e^{-z}}$

\n", + "P($y_i=1|x_i,w$)=$\\sigma(w^Tx_i)$=$\\frac{1}{1+e^{-w^Tx_{i}}}$
\n", + "P($y_i=0|x_i,w$)=$1-\\sigma(w^Tx_i)$=$\\frac{1}{1+e^{w^Tx_{i}}}$
\n", + "Therefore the likelihood of the entire dataset can be given by,
\n", + "P(y|X,w)=$\\prod^{N}_{i=1}P(y_i|x_i,w)=\\prod^{N}_{i=1}\\sigma(w^Tx_i)^{y_i}(1-\\sigma(w^Tx_i)^{y_i})^{1-y_i}$" + ] + }, + { + "cell_type": "markdown", + "id": "a77dfafb-1d5e-4b50-b054-eef235fd4102", + "metadata": {}, + "source": [ + "The prior of the dataset is just P(w)$\\to$N(w|$\\mu,\\epsilon$)
\n", + "where $\\mu$ is the mean and $\\epsilon$ is the covariance matrix\n", + "
\n", + "And the posterior is $P(w|X,y)=\\frac{P(y|X,w).P(w)}{P(y|X)}$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "3782703e-9544-4aa9-9cc8-ef2cbbb2d6cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "true Beta: [ 0.28540966 -0.98083022 -0.06381184 -0.73868922 -0.89687095]\n", + "MAP estimate of beta: [ 0.22168282 -0.84524362 -0.14611654 -0.56873804 -0.75182975]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import math\n", + "from scipy.optimize import minimize\n", + "\n", + "def sigmoid(x):\n", + " return 1/(1+np.exp(-x))\n", + "\n", + "n_samples, n_features = 1000, 5\n", + "X = np.random.randn(n_samples, n_features)\n", + "true_beta = np.random.randn(n_features)\n", + "y = (np.random.rand(n_samples) < sigmoid(np.dot(X ,true_beta))).astype(int)\n", + "\n", + "def negpost(beta,X,mu,sigma,y):\n", + " A = np.dot(X,beta)\n", + " log_likelihood = np.sum(y*np.log(sigmoid(A)) + (1-y)*np.log(1-sigmoid(A)))\n", + " log_prior = -0.5 * np.sum(((beta-mu)/sigma)**2)-(len(beta)/2) * np.log(2 * math.pi * sigma**2)\n", + " return -(log_likelihood + log_prior) \n", + "\n", + "mu_prior=np.zeros(X.shape[1])\n", + "sigma_prior=16\n", + "initial_guess=np.zeros(X.shape[1])\n", + "result=minimize(negpost, initial_guess, args=(X, mu_prior, sigma_prior, y))\n", + "beta_map = result.x\n", + "print(\"true Beta: \",true_beta)\n", + "print(\"MAP estimate of beta: \", beta_map)\n" + ] + }, + { + "cell_type": "markdown", + "id": "62de540a-4277-4a23-8c20-baeb7966f04b", + "metadata": {}, + "source": [ + "
" + ] + }, + { + "cell_type": "markdown", + "id": "2d5e7bb2-e759-4197-83f9-0481c6c8347d", + "metadata": {}, + "source": [ + "**Question 4:**" + ] + }, + { + "cell_type": "markdown", + "id": "de664a03-275b-4d47-ab77-e9d99b3f2fc2", + "metadata": {}, + "source": [ + "**4.1)**
\n", + "For 1 point, there are 2 possible labelings:
\n", + "{1} and {0}
\n", + "The constant function
\n", + "f(x)=1 can classify the point as positive.
f(x)=0 can classify the point as negative
\n", + "shatter any single point.
the set of constant functions can shatter sets of size 0 and 1 but cannot shatter any \n", + "set of size 2 or more, the maximum number of points that can be shattered by the \n", + "set of constant functions is 1. hence, VC dimension of constant functions is 1." + ] + }, + { + "cell_type": "markdown", + "id": "f10c8dab-9d30-4885-9fa8-fad88ae61b1b", + "metadata": {}, + "source": [ + "**4.2)**\n", + "With a single data point, you can't learn anything specific about the linear function.\n", + "With two points, you can potentially learn a line that separates them (if they are not linearly separable, the VC dimension is 0).\n", + "As you add more data points, you can create more complex decision boundaries by adjusting the weights and bias of the hyperplane. However, there's a limit to how many data points you can perfectly classify with a linear function in d dimensions. therefore the VC dimension will be d+1" + ] + }, + { + "cell_type": "markdown", + "id": "7cdf7042-95f7-4be9-ad87-ab2981789f8e", + "metadata": {}, + "source": [ + "**4.3)**
With one data point, you can't determine anything about the rectangle.\n", + "With two points, you can create a rectangle that encloses them
\n", + "With three points, you can potentially create a rectangle that excludes one point while enclosing the other two.
\n", + "With four points, you might encounter a configuration where no axis-aligned rectangle can perfectly classify all points
\n", + "therefore, VC dimension of an axis-aligned rectangle in 2D is 4." + ] + }, + { + "cell_type": "markdown", + "id": "58616093-816a-484b-beee-5e7a87d3ba05", + "metadata": {}, + "source": [ + "**4.4)** A set of two points can be shattered, since there's only a single block of positive examples that could lie within the interval. But no set of 3 points can be shattered, because it can not be labeled in alternating +; - ; + order.Hence VC dimension of intervals is 2." + ] + }, + { + "cell_type": "markdown", + "id": "a00c1c2a-5f21-4f83-b628-bb46c02ad4a2", + "metadata": {}, + "source": [ + "**Question 5:**" + ] + }, + { + "cell_type": "markdown", + "id": "1c4edc67-8e8c-47e8-a4a5-5ab033be0460", + "metadata": {}, + "source": [ + "**5.1)**
$KL(f||g)=\\int[log(f(x))-log(g(x))]f(x)dx$
\n", + "$f(x)=\\frac{1}{\\sqrt{2\\pi}\\sigma_1}e^{\\frac{-1}{2}(\\frac{x-\\mu_1}{\\sigma_1})^2}$
\n", + "$g(x)=\\frac{1}{\\sqrt{2\\pi}\\sigma_2}e^{\\frac{-1}{2}(\\frac{x-\\mu_2}{\\sigma_2})^2}$
\n", + "$log(f(x))-log(g(x))=log(\\frac{\\sigma_2}{\\sigma_1})-0.5(\\frac{x-\\mu_1}{\\sigma_1})^2+0.5(\\frac{x-\\mu_2}{\\sigma_2})^2$
\n", + " =$log(\\frac{\\sigma_2}{\\sigma_1})+0.5(\\frac{(\\sigma_1^2-\\sigma_2^2)x^2+(\\sigma_1^2\\mu_2^2-\\sigma_2^2\\mu_1^2)+...}{(\\sigma_2\\sigma_1)^2})$
\n", + "$KL(f||g)=log(\\frac{\\sigma_2}{\\sigma_1})+\\frac{\\sigma_1^2+(\\mu1-\\mu2)^2}{2\\sigma_2^2}-\\frac{1}{2}$
" + ] + }, + { + "cell_type": "markdown", + "id": "3ad5f7bf-af7b-4ded-b1c4-ddec06c75731", + "metadata": {}, + "source": [ + "**5.3)**
\n", + "KL divergence capture the additional data needed to represent one probability distribution(p) in terms of another(q) assuming q is the true distribution. A higher KL divergence value indicates a large difference between the two distributions." + ] + }, + { + "cell_type": "markdown", + "id": "545cb119-4637-4b10-82b8-2eb20c9a7c79", + "metadata": {}, + "source": [ + "**Question 6:**" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "ae2fbf3e-74ca-4434-943e-08e786373985", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.45511241e-013 0.00000000e+000 0.00000000e+000 ... 2.14659638e-005\n", + " 1.05125455e-253 3.68908344e-217]\n", + "[1.45869159e-013 0.00000000e+000 0.00000000e+000 ... 2.14405072e-005\n", + " 1.18894007e-253 4.09687480e-217]\n", + "[-3.57917859e-016 0.00000000e+000 0.00000000e+000 ... 2.54565717e-008\n", + " -1.37685513e-254 -4.07791359e-218]\n" + ] + }, + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Unnamed: 0 data para\n", + "324 324 4.265624 -8.283114e-12\n", + "7763 7763 4.265821 -8.278843e-12\n", + "2153 2153 4.266086 -8.269104e-12\n", + "1148 1148 4.264565 -8.266170e-12\n", + "6781 6781 4.264327 -8.253822e-12\n", + "... ... ... ...\n", + "6555 6555 4.688447 1.098229e-02\n", + "2652 2652 4.692392 1.098726e-02\n", + "4927 4927 4.691943 1.098852e-02\n", + "6579 6579 4.690387 1.098927e-02\n", + "7552 7552 4.691109 1.098962e-02\n", + "\n", + "[8000 rows x 3 columns]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "df=pd.read_csv(r'data_open.csv')\n", + "\n", + "first_half = df['data'][:4000].reset_index(drop=True)\n", + "second_half = df['data'][4000:].reset_index(drop=True)\n", + "data=df['data']\n", + "\n", + "#intialisation\n", + "mu1=first_half.mean()\n", + "mu2=second_half.mean()\n", + "sigma1=np.sqrt(first_half.var())\n", + "sigma2=np.sqrt(second_half.var())\n", + "prior1=np.full(8000,0.5)\n", + "prior2=np.full(8000,0.5)\n", + "resp1=np.full(8000,0.5) #posteriors\n", + "resp2=np.full(8000,0.5)\n", + "curr_log_likelihood=np.sum(np.log(prior1))+np.sum(np.log(prior2))\n", + "\n", + "def pdf(x,mu,sigma):\n", + " return 1/(sigma * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2 / (2 * sigma**2))\n", + "\n", + "#convergence conditions\n", + "tolerance=1e-6\n", + "prev_log_likelihood=-np.inf\n", + "\n", + "for j in range(100):\n", + " prev_log_likelihood=curr_log_likelihood\n", + " for i in range(0,8000):\n", + " resp1[i]=pdf(data[i],mu1,sigma1)*prior1[i]/(prior1[i]+prior2[i])\n", + " resp2[i]=pdf(data[i],mu2,sigma2)*prior2[i]/(prior1[i]+prior2[i])\n", + " mu1=np.average(data,weights=resp1)\n", + " mu2=np.average(data,weights=resp2)\n", + " sigma1=np.sqrt(np.average((data-mu1)**2,weights=resp1))\n", + " sigma2=np.sqrt(np.average((data-mu2)**2,weights=resp2))\n", + " prior1=np.full(8000,np.average(resp1))\n", + " prior2=np.full(8000,np.average(resp2))\n", + "\n", + "difference_array=resp1-resp2\n", + "print(resp1)\n", + "print(resp2)\n", + "print(difference_array)\n", + "df['para']=difference_array\n", + "sorted_df=df.sort_values(by='para')\n", + "N1=sorted_df['data'][:4000].reset_index(drop=True)\n", + "N2=sorted_df['data'][4000:].reset_index(drop=True)\n", + "sorted_df.head(8000)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c187563e-0a1e-48f8-8d91-fa9838285c5a", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Assignment-3.ipynb b/Assignment-3.ipynb new file mode 100644 index 0000000..7fc46e0 --- /dev/null +++ b/Assignment-3.ipynb @@ -0,0 +1,279 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "123fc965-6d52-47b2-8b43-a75c9f98c5ef", + "metadata": {}, + "source": [ + "**Question 1:**
\n" + ] + }, + { + "cell_type": "markdown", + "id": "d0735b2e-2a7b-4e3f-8a2c-ced4a26d633c", + "metadata": {}, + "source": [ + "**1.1)**
\n", + "using second order taylor approximation:
\n", + "$f(x)=f(x^*)+\\frac{1}{2}(x-x^*)H_{f}(x^*)(x-x^*)$, where $x^*$ is critical point
\n", + "using the update rule near $x^*$:\n", + "
$x_{k+1}=x_k-\\alpha H_f(x^*)(x_k-x^*)$
\n", + "$x_{k+1}-x^*=(I-\\alpha H_f(x^*))(x_k-x^*)$
\n", + "We can infer from the update equation that the eigen values of $(I-\\alpha H_f(x^*))$ must lie within the unit circle in complex plane so that the perturbations around $x^*$ diminish rather than grow
Therefore,
\n", + "$-1<1-\\alpha\\lambda_i<1$
\n", + "$0<\\alpha<\\frac{2}{\\lambda_{max}}$
\n", + "the range of stable learning rate is (0,$\\frac{2}{\\lambda_{max}}$)
\n", + "and the critical learning rate is $\\frac{2}{\\lambda_{max}}$, where $\\lambda_{max}$ is the largest eigen value of the Hessian matrix H" + ] + }, + { + "cell_type": "markdown", + "id": "dbb88b1e-7623-4cc7-b08f-d1556349ed14", + "metadata": {}, + "source": [ + "**1.2)**
\n", + "given,
$f(x)=\\frac{1}{2}x^Tax+bx+c$
\n", + "using update rule,
\n", + "$x_{n+1}=x_{n}-\\alpha\\nabla_{x_n}f(x)$
\n", + "substituting $\\nabla f(x)=ax+b$ is update gives,
\n", + "$x_{n+1}=x_{n}-\\alpha ax_n-\\alpha b$
\n", + "$x_{n+1}=x_n(1-\\alpha a)-\\alpha b$
\n", + "we can neglect the constant vector here,
\n", + "from derivation above replacing Hessian with $a$ we get a similar result,
\n", + "$0<\\alpha<\\frac{2}{\\lambda_{max}}$
\n", + "the range of stable learning rate is (0,$\\frac{2}{\\lambda_{max}}$)
\n", + "and the critical learning rate is $\\frac{2}{\\lambda_{max}}$, where $\\lambda_{max}$ is the largest eigen value of the matrix $a$" + ] + }, + { + "cell_type": "markdown", + "id": "e06144fb-9d08-4a59-9264-99541e8ad2cd", + "metadata": {}, + "source": [ + "**1.3)**" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "c8c7a4c0-bd86-44f4-972e-53395f6b939b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Function and its gradient\n", + "def f(x1, x2):\n", + " return 9*x1**2 + 4*x2**2 + 36*x1*x2 + 9*x1 + 4*x2 + 10\n", + "\n", + "def grad_f(x1, x2):\n", + " dfdx1 = 18*x1 + 36*x2 + 9\n", + " dfdx2 = 8*x2 + 36*x1 + 4\n", + " return np.array([dfdx1, dfdx2])\n", + "\n", + "# Gradient Descent\n", + "def gradient_descent(starting_point, learning_rate, num_iterations):\n", + " x = starting_point\n", + " points = [x]\n", + " for i in range(num_iterations):\n", + " grad = grad_f(x[0], x[1])\n", + " x = x - learning_rate * grad\n", + " points.append(x)\n", + " return np.array(points)\n", + "\n", + "# Parameters\n", + "starting_point = np.array([5.0, 5.0])\n", + "num_iterations = 60\n", + "\n", + "# Learning rates\n", + "critical = 0.04 # Adjust this value based on eigenvalue calculation if necessary\n", + "zero = 0.00001\n", + "outside = 3.0\n", + "\n", + "# Perform gradient descent for each learning rate\n", + "crit_gd = gradient_descent(starting_point, critical, num_iterations)\n", + "zero_gd = gradient_descent(starting_point, zero, num_iterations)\n", + "max_gd = gradient_descent(starting_point, outside, num_iterations)\n", + "\n", + "# Plotting the results\n", + "plt.figure(figsize=(12, 8))\n", + "\n", + "if len(crit_gd) > 0:\n", + " plt.plot(crit_gd[:, 0], crit_gd[:, 1], label='Critical')\n", + " plt.scatter(crit_gd[:, 0], crit_gd[:, 1])\n", + "\n", + "# Adjust the axis limits\n", + "plt.xlabel('$x_1$')\n", + "plt.ylabel('$x_2$')\n", + "plt.title('Gradient Descent Trajectories')\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "76b0502a-02ff-48ec-9239-a493481fc37e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(12, 8))\n", + "if len(zero_gd) > 0:\n", + " plt.plot(zero_gd[:, 0], zero_gd[:, 1], label='Approaching Zero',color='green')\n", + " plt.scatter(zero_gd[:, 0], zero_gd[:, 1],color='green')\n", + " \n", + "# Adjust the axis limits\n", + "plt.xlabel('$x_1$')\n", + "plt.ylabel('$x_2$')\n", + "plt.title('Gradient Descent Trajectories')\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "16a55cf1-22ad-4854-84a2-6ef436db4dcd", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(12, 8))\n", + "if len(max_gd) > 0:\n", + " plt.plot(max_gd[:, 0], max_gd[:, 1], label='Beyond Stability',color='red')\n", + " plt.scatter(max_gd[:, 0], max_gd[:, 1],color='red')\n", + "\n", + "# Adjust the axis limits\n", + "plt.xlabel('$x_1$')\n", + "plt.ylabel('$x_2$')\n", + "plt.title('Gradient Descent Trajectories')\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "58525232-1527-468e-addf-682ba0c9ec0f", + "metadata": {}, + "source": [ + "**Question 2:**
\r\n", + "the primal problem is:
\r\n", + "maximise $50x_1+60x_2$
\r\n", + "subject to
\r\n", + "$2x_{1}+x_{2}+x_{3}=300$
\r\n", + "$3x_1 + 4x_2 + x_4 = 509$
\r\n", + "$4x_1 + 7x_2 + x_5 = 812$
\r\n", + "$x_1 \\geq 0$
\r\n", + "$x_2 \\geq 0$
\r\n", + "$x_3 \\geq 0$
\r\n", + "$x_4 \\geq 0$
\r\n", + "$x_5 \\geq 0$
\r\n", + "the lagrangian fuction is:\r\n", + "$L(x_1,x_2,x_3,x_4,x_5,\\lambda_1,\\lambda_2,\\lambda_3)$=\r\n", + "$50x_1+60x_2+\\lambda_1(300-2x_1 - x_2 - x_3)+\\lambda_2(-3x_1 - 4x_2 - x_4 + 509)+\\lambda_3(812-4x_1 - 7x_2 - x_5)$
\r\n", + "expanding and simplyfying:
\r\n", + "$L=(50-2\\lambda_1-3\\lambda_2-4\\lambda_3)x_1+(60-\\lambda_1-4\\lambda_2-7\\lambda_3)x_2-\\lambda_1x_3-\\lambda_2x_4-\\lambda_3x_5+300$
\r\n", + "\r\n", + "**Dual function:**
\r\n", + "for $x_1$:
\r\n", + "$50-2\\lambda_1-3\\lambda_2-4\\lambda_3\\leq0$
\r\n", + "for $x_2$:
\r\n", + "$60-\\lambda_1-4\\lambda_2-7\\lambda_3\\leq0$
\r\n", + "for $x_3,x_4,x_5$:
\r\n", + "$\\lambda_1\\geq0\\lambda_2\\geq0,\\lambda_3\\geq0$
\r\n", + "therefore,
\r\n", + "the lagrangian dual for the problem is:
\r\n", + "Minimize $300\\lambda_1+509\\lambda_2+812\\lambda_3$
\r\n", + "subject to:
\r\n", + "$50-2\\lambda_1-3\\lambda_2-4\\lambda_3\\leq0$
\r\n", + "$60-\\lambda_1-4\\lambda_2-7\\lambda_3\\leq0$
\r\n", + "$\\lambda_1\\geq0,\\lambda_2\\geq0,\\lambda_3\\geq0$
\r\n", + "
\r\n", + "Now to apply simplex algorithm let us first convert the problem into standard form,
\r\n", + "Maximise $-300\\lambda_1-509\\lambda_2-812\\lambda_3$
\r\n", + "subject to:
\r\n", + "$50-2\\lambda_1-3\\lambda_2-4\\lambda_3\\leq0$
\r\n", + "$60-\\lambda_1-4\\lambda_2-7\\lambda_3\\leq0$
\r\n", + "$\\lambda_1\\geq0,\\lambda_2\\geq0,\\lambda_3\\geq0$
\r\n", + "
\r\n", + "Now converting into slack form,
\r\n", + "Z = $-300\\lambda_1-509\\lambda_2-812\\lambda_3$
\r\n", + "$c_1=-50+2\\lambda_1+3\\lambda_2+4\\lambda_3$
\r\n", + "$c_2=-60+\\lambda_1+4\\lambda_2+7\\lambda_3$
\r\n", + "$\\lambda_1\\geq0,\\lambda_2\\geq0,\\lambda_3\\geq0$
\r\n", + "
\r\n", + "Taking basic variables as $\\lambda_3,c_1,c_2$
\r\n", + "we get a basic feasible solution as (4,14,0,0,0)\r\n", + "

\r\n", + "Simplex Tableau:mbda_2\\geq0,\\lambda_3\\geq0$
mbda_2\\geq0,\\lambda_3\\geq0$
3\\geq0$
_2 - x_5)$
\r\n", + "x5 ≥0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "18885e57-0e8a-4341-b8cf-6cd8bf9f914f", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Assignment-4.ipynb b/Assignment-4.ipynb new file mode 100644 index 0000000..d6afac5 --- /dev/null +++ b/Assignment-4.ipynb @@ -0,0 +1,613 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f0450b20-621f-487d-9d9e-2b480bb912aa", + "metadata": {}, + "source": [ + "**Linear and Logistic Regression**" + ] + }, + { + "cell_type": "markdown", + "id": "b4e92daa-6ed3-4121-bb5f-1863526f97b5", + "metadata": {}, + "source": [ + "**Question 1:**
\n", + "**Part a:**
\n", + "We usually estimate the mean of P(y∣X) because we aim to express the value of y in terms of x. Given the features X, the distribution P(y∣X) provides a reliable estimate of the expected value of y, which is often the most useful summary of the relationship between y and X for prediction and interpretation purposes
" + ] + }, + { + "cell_type": "markdown", + "id": "837f2f56-5b46-4cb3-a652-3a93d5e81e8f", + "metadata": {}, + "source": [ + "**Part b:**" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e854f568-275f-4a7e-9784-6b16b4e4d0b1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "class LinearRegression:\n", + " def __init__(self):\n", + " self.weights = None\n", + " \n", + " def fit(self, X, y):\n", + " X_b = np.c_[np.ones((X.shape[0], 1)), X]\n", + " self.weights = np.linalg.inv(X_b.T @ X_b) @ X_b.T @ y\n", + " \n", + " def predict(self, X):\n", + " X_b = np.c_[np.ones((X.shape[0], 1)), X]\n", + " return X_b @ self.weights\n", + "\n", + "np.random.seed(42)\n", + "X = 2 * np.random.rand(100, 1)\n", + "y = 4 + 3 * X + np.random.randn(100, 1)\n", + "\n", + "model = LinearRegression()\n", + "model.fit(X, y)\n", + "\n", + "a=np.arange(0,2.5)\n", + "plt.scatter(X,y,color='red')\n", + "plt.plot(a,model.predict(a),color='blue')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "29492ef2-83ac-41a9-a517-7606e2bbfed1", + "metadata": {}, + "source": [ + "parameterizing $\\sigma$ can be useful when errors are more widely distributed, it provides more acuurate uncertainity estimates but the cons of parameterizing $\\sigma$ is that the normal equation for calculating weights cannot be used and a recursive optimization method should be used which increases complexity, it may also lead to overfitting." + ] + }, + { + "cell_type": "markdown", + "id": "f06beafd-ee4a-408e-bf18-f427a77f2035", + "metadata": {}, + "source": [ + "**Question 2:**" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "51c33724-092e-4b24-9985-65f44b13c523", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "A_train=pd.read_csv(\"train_set_A.csv\")\n", + "A_test=pd.read_csv(\"test_set_A.csv\")\n", + "B_train=pd.read_csv(\"train_set_B.csv\")\n", + "B_test=pd.read_csv(\"test_set_B.csv\")\n", + "C_train=pd.read_csv(\"train_set_C.csv\")\n", + "C_test=pd.read_csv(\"test_set_C.csv\")" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1afa84d3-6f94-4470-b240-e7896003262f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
LinearRegression()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "LinearRegression()" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.linear_model import LinearRegression\n", + "model_a=LinearRegression()\n", + "model_a.fit(A_train[['x']],A_train[['y']])" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "54d1ecc2-f343-4306-a37f-4d951c5fd3fa", + "metadata": {}, + "outputs": [], + "source": [ + "a_a=model_a.predict(A_test[['x']])\n", + "a_b=model_a.predict(B_test[['x']])\n", + "a_c=model_a.predict(C_test[['x']])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "3f2ea54c-7e5c-43eb-8758-08847614fe24", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
LinearRegression()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "LinearRegression()" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model_b=LinearRegression()\n", + "model_b.fit(B_train[['x']],B_train[['y']])" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "97ebdce3-0b18-4ad0-8719-86af39b1e7fd", + "metadata": {}, + "outputs": [], + "source": [ + "b_a=model_b.predict(A_test[['x']])\n", + "b_b=model_b.predict(B_test[['x']])\n", + "b_c=model_b.predict(C_test[['x']])" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "d7c1f393-025e-4ab0-80f5-52e020c19639", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
LinearRegression()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "LinearRegression()" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model_c=LinearRegression()\n", + "model_c.fit(C_train[['x']],C_train[['y']])" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "a3a0493c-b839-4d0a-a225-d39825fc3d69", + "metadata": {}, + "outputs": [], + "source": [ + "c_a=model_c.predict(A_test[['x']])\n", + "c_b=model_c.predict(B_test[['x']])\n", + "c_c=model_c.predict(C_test[['x']])" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "d68eda18-6b54-44e3-8575-720544306ff1", + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.metrics import mean_squared_error" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "1ef363bb-b582-45a5-bd34-c122baaff3c0", + "metadata": {}, + "outputs": [], + "source": [ + "aa_err=(a_a-A_test[['y']])\n", + "ba_err=(b_a-A_test[['y']])\n", + "ca_err=(c_a-A_test[['y']])\n", + "ab_err=(a_b-B_test[['y']])\n", + "bb_err=(b_b-B_test[['y']])\n", + "cb_err=(c_b-B_test[['y']])\n", + "ac_err=(a_c-C_test[['y']])\n", + "bc_err=(b_c-C_test[['y']])\n", + "cc_err=(c_c-C_test[['y']])" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "15c4730f-e236-4ec5-b8ae-b0b8b57597f4", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "ae13dcd2-4097-4b56-b864-3c6389642a8f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig,axs=plt.subplots(3,3,figsize=(15,15))\n", + "datasets=[[aa_err,ab_err,ac_err],[ba_err,bb_err,bc_err],[ca_err,cb_err,cc_err]]\n", + "dict={0:\"A\",1:\"B\",2:\"C\"}\n", + "for i in {0,1,2}:\n", + " for j in {0,1,2}:\n", + " ax=axs[i,j]\n", + " ax.hist(datasets[i][j],bins=30,alpha=0.75,color=\"blue\",edgecolor=\"black\")\n", + " ax.set_title(f\"model {dict[i]}, test {dict[j]}\")\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "f675030b-2056-40db-ad54-0e376b660cfc", + "metadata": {}, + "source": [ + "**Question 3:**" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "be8da1f3-b503-4c67-8bfc-5e6ad36d29a3", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "n_samples=100\n", + "Xclass0=np.random.randn(n_samples,2)+np.array([-2,-2])\n", + "Xclass1=np.random.randn(n_samples,2)+np.array([2,2])\n", + "X=np.vstack((Xclass0,Xclass1))\n", + "Y=np.hstack((np.zeros(n_samples),np.ones(n_samples)))" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "92158016-86d5-496b-b9fb-e303b19a8a7f", + "metadata": {}, + "outputs": [], + "source": [ + "def g(z):\n", + " return 1/(1+np.exp(-z))\n", + "def loglikelihood(x,y,theta):\n", + " z = np.dot(x, theta)\n", + " z = np.clip(g(z), 1e-15, 1-1e-15)\n", + " logl = np.mean(y*np.log(z)+(1-y)*np.log(1-z))\n", + " return logl\n", + "def pred(x,theta):\n", + " return g(np.dot(x,theta))\n", + "def pred_bin(x,theta):\n", + " z=g(np.dot(x,theta))\n", + " return (z>=0.5).astype(int)\n", + "def batchgd(x,y,theta,n_iter=100):\n", + " alpha=0.1\n", + " errors=[]\n", + " for i in range(0,n_iter):\n", + " theta=(theta+alpha*np.dot((y-pred(x,theta)),x))\n", + " error=loglikelihood(x,y,theta)\n", + " errors.append(error)\n", + " return theta,errors\n", + "def newton_method(x, y,theta, n_iter=50):\n", + " errors = []\n", + " for i in range(0,n_iter):\n", + " predictions = pred(x,theta)\n", + " error = loglikelihood(x, y, theta)\n", + " errors.append(error)\n", + " gradient = -np.dot((y-pred(x,theta)),x)\n", + " w = np.diag(predictions*(1-predictions))\n", + " hessian = np.dot(np.dot(x.T, w), x)\n", + " theta = theta-np.dot(np.linalg.inv(hessian), gradient)\n", + " return theta, errors" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "9e9184a7-da67-4c3a-85a1-77467543d5c5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "accuracy using gradient descent: 0.995 with run-time: 0.012635231018066406\n", + "accuracy using newton method: 0.995 with run-time: 0.02735447883605957\n" + ] + } + ], + "source": [ + "from sklearn.metrics import accuracy_score\n", + "import time\n", + "theta=np.array([1,1])\n", + "start_time_gd = time.time() \n", + "weights_gd, errors_gd = batchgd(X, Y,theta)\n", + "end_time_gd = time.time()\n", + "run_time_gd = end_time_gd-start_time_gd\n", + "theta=np.array([1,1])\n", + "start_time_nm = time.time()\n", + "weights_nm, errors_nm = newton_method(X, Y,theta)\n", + "end_time_nm = time.time()\n", + "run_time_nm = end_time_nm-start_time_nm\n", + "pred_gd = pred_bin(X, weights_gd)\n", + "pred_nm = pred_bin(X, weights_nm)\n", + "accuracy_gd = accuracy_score(Y, pred_gd)\n", + "accuracy_nm = accuracy_score(Y, pred_nm)\n", + "print(f'accuracy using gradient descent: {accuracy_gd} with run-time: {run_time_gd}')\n", + "print(f'accuracy using newton method: {accuracy_nm} with run-time: {run_time_nm}')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "dcdc5e96-a7e9-4597-bac2-08ff6ff847d9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "x1 = np.arange(0, 100)\n", + "x2 = np.arange(0, 50)\n", + "plt.plot(x1, errors_gd, color='red', label='loglikelihood function using gd')\n", + "plt.plot(x2, errors_nm, color='blue', label='loglikelihood function using nm')\n", + "plt.xlabel('iterations')\n", + "plt.ylabel('cost function')\n", + "plt.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "58be64e0-48ac-4212-bae0-11928d73566b", + "metadata": {}, + "source": [ + "as we can see from the plot that newtons method reaches a higher value much quicker but consumes more time and as features increase the time taken will go higher because the complexity of calculating the inverse of the hessian gets more and more complex but for only 2 features newtons method is much better than batch gradient descent" + ] + }, + { + "cell_type": "markdown", + "id": "5053a2ac-bdce-46ec-9436-47099bde55a1", + "metadata": {}, + "source": [ + "**Question 4:**

\n", + "**a)** With a large sample size n, flexible methods can learn complex patterns in the data without overfitting, as the large number of observations provides sufficient information to estimate the relationship between the predictors and the response.Flexible methods typically have lower bias but higher variance. However, when n is large, the variance of the flexible method decreases because the model has enough data to generalize well. The overall error is minimized when the bias is low.

\n", + "**b)** When p is large and n is small, flexible methods are prone to overfitting because they can capture noise in the data, leading to poor generalization to new data. Inflexible methods have higher bias and lower variance thus less likely to overfit and perform better for a small value of n\n", + "

\n", + "**c)** flexible methods are better at capturing complex and non-linear relationships in the data than inflexble methods. the non linearity in the data causes inflexible methods to have large biases and although flexible methods have larger variance, they have much lower bias and hence work better." + ] + }, + { + "cell_type": "markdown", + "id": "ec0ea36f-a6bc-4827-a470-5146c09391d5", + "metadata": {}, + "source": [ + "**Exponential families and GLM's**" + ] + }, + { + "cell_type": "markdown", + "id": "c0f472e5-8a6b-410e-8eae-85badcbc98ac", + "metadata": {}, + "source": [ + "**Question 1:**" + ] + }, + { + "cell_type": "markdown", + "id": "fb0d1f19-e912-4bf5-b9bc-8aeb17591add", + "metadata": {}, + "source": [ + "**Part a)**
$p(y;\\phi)=(1-\\phi)^{y-1}\\phi$
\n", + "$p(y;\\phi)=e^{(y-1)log(1-\\phi)+log(\\phi)}$
\n", + "comparing with the exponential family
\n", + "$b(y)=1$
\n", + "$T(y)=y$
\n", + "$\\eta=log(1-\\phi)$
\n", + "$a(\\eta)=log(\\frac{\\phi}{1-\\phi})=log(e^{-\\eta}-1)$" + ] + }, + { + "cell_type": "markdown", + "id": "3b752a3a-156c-43c4-90cb-8c83c098454d", + "metadata": {}, + "source": [ + "**Part b)**
\n", + "the mean of the relationship is given by $\\mu=\\frac{1-\\phi}{\\phi}$
\n", + "therefore the canonical link function $g(\\mu)$ is:
\n", + "$g(\\mu)=log(\\mu+1)$" + ] + }, + { + "cell_type": "markdown", + "id": "1fd256bf-64c4-4316-8503-0b2a4ffae6e9", + "metadata": {}, + "source": [ + "**Part c)**
\n", + "$log(P(y|x;\\theta))=y(x^T.\\theta)-log(e^{-x^T.\\theta}-1)$,
\n", + "differentiating wrt to $\\theta_j$ :
\n", + "$\\frac{\\partial logp(y|x;\\theta)}{\\partial \\theta_j}= yx_j+(\\frac{e^{x^T\\theta}}{e^{x^T\\theta}-1})x_j$\n", + "
this gives the gradient ascent update rule as:
\n", + "$\\theta_j=\\theta_j+\\alpha(y.x_j+(\\frac{e^{x^T\\theta}}{e^{x^T\\theta}-1})x_j)$" + ] + }, + { + "cell_type": "markdown", + "id": "4f6d82f5-56a7-4de9-81c2-0f0ff373094b", + "metadata": {}, + "source": [ + "**Question 2:**" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "0f982877-3fa5-46b1-818d-2957a8d99a42", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean Squared Error: 67.36738622079729\n" + ] + }, + { + "data": { + "image/png": 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L+e1vf5vq5gghBoHk7Aghhq1QKHRQXs8f/vAHOjs7D1paQwgxfEnPjhBi2Fq7di0333wzX/ziF8nMzOTdd9/l97//PRUVFWzcuHFYLJ4qhDgySVAWQgxbpaWlFBcXs3z5cjo7O8nIyOCKK67ggQcekEBHiJOI9OwIIYQQYliTnB0hhBBCDGsS7AghhBBiWJOcHRKlqI2NjbhcLpn+XAghhDhB6LqO3++noKDgsBNsSrADNDY2UlxcnOpmCCGEEOITqK+vP+xiuhLsAC6XC0h8WG63O8WtEUIIIcTR8Pl8FBcXJ7/HD0WCHT5audftdkuwI4QQQpxgjpSCIgnKQgghhBjWJNgRQgghxLAmwY4QQgghhjXJ2TlKmqYRiURS3QzxKZnN5sOWJwohhBh+JNg5CpFIhN27d6NpWqqbIj4lVVUZOXKkrIskhBAnEQl2jkDXdZqamjAYDBQXF0uvwAmsb/LIpqYmSkpKZAJJIYQ4SUiwcwSxWIze3l4KCgqw2+2pbo74lLKzs2lsbCQWi2EymVLdHCGEEINAuimOIB6PA8iwxzDR93vs+70KIYQY/iTYOUoy5DE8yO9RCCFOPjKMJYQQQojjQ9Ogrg78fnC5oKQEUpD7KsGOoLS0lJtuuombbrop1U05Jobb8wghxAmpqgpWroTt2yEUAqsVxo2Diy6CiopBbYoMYw1z9fX1fO1rX6OgoACz2cyIESP49re/TUdHR6qbJoQQYriqqoLly2HTJsjKgrFjEz83bUpsr6oa1OZIsDNINE2nvrOX7c0+6jt70TT9uN9z165dnHrqqVRXV/OnP/2JmpoaHnvsMV566SVmzJhBZ2fncW/DQOLxuMxZJIQQw5WmJXp02tuhshLcbjAYEj8rKxPbV61KHDdIJNgZBDWtfh5dW8vP1+xk+UvV/HzNTh5dW0tNq/+43nfp0qWYzWZeeOEFZs2aRUlJCfPnz+fFF1+koaGB/+//+/+Sx/r9fr785S/jcDgoLCzk4YcfTu7TdZ27776bkpISLBYLBQUF3Hjjjcn94XCY2267jcLCQhwOB9OnT2ft2rXJ/Y8//jhpaWn885//pLKyEovFwu9+9zusVivd3d392vztb3+bc889N/n+9ddf58wzz8Rms1FcXMyNN95IIBBI7m9tbeXCCy/EZrMxcuRInnzyyWP4CQohhPjY6uoSQ1fFxXBgUYiiQFFRomenrm7QmiTBznFW0+pnxRt72NLoJc1uYlSWkzS7iS2NXla8see4BTydnZ2sXr2ab33rW9hstn778vLyWLx4MX/5y1/Q9UQP009+8hMmT57Mpk2b+O53v8u3v/1t1qxZA8AzzzzDz3/+c37zm99QXV3NqlWrmDhxYvJ6119/PevXr+fPf/4zH3zwAV/84heZN28e1dXVyWN6e3v58Y9/zO9+9zu2bt3K4sWLSUtL45lnnkkeE4/H+ctf/sLixYsBqK2tZd68eSxatIgPPviAv/zlL7z++utcf/31yXOuvPJK6uvreeWVV/jb3/7GI488Qmtr67H/QIUQQhwdvz+Ro+NwDLzf4Ujs9x/ff/DvTxKUjyNN01m9pYXOQITROc5k2bPLasJpMVLd2sMLW1sYleVEVY9tSXR1dTW6rlNxiCSwiooKurq6aGtrA2DmzJl897vfBWDMmDG88cYb/PznP+f888+nrq6OvLw8Zs+ejclkoqSkhNNPPx2Auro6VqxYQV1dHQUFBQDcdttt/Oc//2HFihX86Ec/AiAajfLII48wefLkZBsuu+wynnrqKa6++moAXnrpJbq7u1m0aBEAy5YtY/HixclE49GjR7N8+XJmzZrFo48+Sl1dHc8//zxvvfUWp512GgC///3vD/nMQgghBoHLlUhGDgQSQ1cHCgQS+12uQWuS9OwcRw3dQWrbesj3WA+a30VRFPI9Vmpae2joDh63NvT13BzJjBkzDnpf9WEC2Re/+EWCwSCjRo3immuuYeXKlcRiMQA2b95MPB5nzJgxOJ3O5GvdunXU1tYmr2c2m5k0aVK/eyxevJi1a9fS2NgIwJNPPsmCBQtIS0sD4P333+fxxx/vd925c+eiaRq7d++mqqoKo9HItGnTktccN25c8nwhhBApUFKSqLqqr4cDv4N0HfbtS1RjlZQMWpOkZ+c4CkRihGJx7GbbgPttZgMtvhCBSOyY37u8vBxFUaiqquKiiy46aH9VVRXp6elkZ2cf8VrFxcXs2LGDF198kTVr1vCtb32Ln/zkJ6xbt46enh4MBgMbN27EYDD0O8/pdCb/bLPZDgr4TjvtNMrKyvjzn//Mddddx8qVK3n88ceT+3t6evjGN77RLz+oT0lJCTt37jxi24UQQgwyVU2Ul9fXw7ZtiRwdhyPRo7NvX6Iqa+HCQZ1vR4Kd48hhNmI1GuiNxHBZD16HKRiJYzEacJiP/a8hMzOT888/n0ceeYSbb765X95Oc3MzTz75JFdccUUyAHnzzTf7nf/mm2/2Gw6y2WxceOGFXHjhhSxdupRx48axefNmpkyZQjwep7W1lTPPPPNjt3Px4sU8+eSTFBUVoaoqCxYsSO6bOnUq27Zto7y8fMBzx40bRywWY+PGjclhrB07dhyU9CyEEOL40DSdhu4ggUgMh9lIYZotkZZRUQE33vjRPDsNDYmhq6lTE4HOIKcbSLBzHBWm2SjLdrKl0YvTYuzXs6HrOk3eEBMLPRSmDdzz82n9+te/5jOf+Qxz587lhz/8ISNHjmTr1q3cfvvtFBYWcv/99yePfeONN3jwwQdZuHAha9as4emnn+bf//43kKimisfjTJ8+Hbvdzh//+EdsNhsjRowgMzOTxYsXc8UVV/DQQw8xZcoU2traeOmll5g0aVK/4GUgixcv5u677+b+++/nkksuwWKxJPfdcccdnHHGGVx//fV8/etfx+FwsG3bNtasWcOvf/1rxo4dy7x58/jGN77Bo48+itFo5KabbjooIVsIIcSxV9PqZ/WWFmrbegjF4liNBsqyncydkEt5jisR0IwdOyRmUJacneNIVRXmTsglw2GmurUHfyhKTNPwh6JUt/aQ4TAzZ3zuMU9O7jN69GjeeecdRo0axaWXXkpZWRnXXnst55xzDuvXrycjIyN57K233so777zDlClT+OEPf8jPfvYz5s6dC0BaWhq//e1vmTlzJpMmTeLFF1/kX//6F5mZmQCsWLGCK664gltvvZWxY8eycOFC3n77bUqOYjy2vLyc008/nQ8++CBZhdVn0qRJrFu3jp07d3LmmWcyZcoUvv/97ycTofvuXVBQwKxZs7j44ou59tprycnJORYfnxBCiEM46kpjVYXSUpg4MfEzBYEOgKIfbQbrMObz+fB4PHi9XtwHZI6HQiF2797NyJEjsVqtn+j6+0e/4Vhi6Ko8x8mc8R9Gv2LQHIvfpxBCnMw0TefRtbVsafT2qzSGxKhFdWsPEws9fHNW2XH7x3yfw31/70+GsQZBeY6LUWc7Bx7XFEIIIU4gH6fSuDjDnqJW9ifBziBRVWXI/NKFEEKITyqVlcaflOTsCCGEEOKo7V9pPJDjWWn8SUmwI4QQQoij1ldp3OQNHTRxbV+lcXmOk8I0W0oWwR7I0Am7hBBCCDHk9VUaN3qDVLcmcndsZgPBSJwmbyhZabyrvefwpemDSIIdIYQQQnws5TkurppZmgxmWnwhLEYDEws9zBmfC8CKN/bQGYiQ77FiN9vojcTY0uil0RvkqpmlgxrwSLAjhBBCiI/tUJXGAI+urU3JItiHIsGOEEIIIT6RgSqN6zt7h1xpuiQoCyGEEOKY+ag0feD+FJvZQDgWH9TSdAl2xKdy5ZVXsnDhwuT7s88+m5tuumnQ27F27VoURZFFQIUQIsWGYmm6BDvD1JVXXomiKCiKgtlspry8nHvvvZdY7PhG0n//+9+57777jupYCVCEEGL4+Til6YNFcnYGi6YN+sqv8+bNY8WKFYTDYZ577jmWLl2KyWTizjvv7HdcJBLBbDYfk3vuv7ioEEKIk8/RlqYP5pJJKe3ZefTRR5k0aRJutxu3282MGTN4/vnnk/vPPvvsZO9E3+ub3/xmv2vU1dWxYMEC7HY7OTk53H777ce99+Jjq6qCBx6A738f7rsv8fOBBxLbjyOLxUJeXh4jRozguuuuY/bs2fzzn/9MDj3df//9FBQUMHbsWADq6+u59NJLSUtLIyMjgy984Qvs2bMneb14PM4tt9xCWloamZmZfOc73zkoaj9wGCscDnPHHXdQXFyMxWKhvLyc3//+9+zZs4dzzjkHgPT0dBRF4corrwRA0zSWLVvGyJEjsdlsTJ48mb/97W/97vPcc88xZswYbDYb55xzTr92CiGESK2+0vQJBR66e6PsaQ/Q3RtlYqFn0MvOIcU9O0VFRTzwwAOMHj0aXdd54okn+MIXvsCmTZsYP348ANdccw333ntv8hy7/aPM7Xg8zoIFC8jLy+O///0vTU1NXHHFFZhMJn70ox8N+vMMqKoKli+H9nYoLgaHAwIB2LQJ6uvhxhuhomJQmmKz2ejo6ADgpZdewu12s2bNGgCi0Shz585lxowZvPbaaxiNRn74wx8yb948PvjgA8xmMw899BCPP/44/+///T8qKip46KGHWLlyJeeee+4h73nFFVewfv16li9fzuTJk9m9ezft7e0UFxfzzDPPsGjRInbs2IHb7cZmS3RpLlu2jD/+8Y889thjjB49mldffZWvfvWrZGdnM2vWLOrr67n44otZunQp1157Le+88w633nrr8f8AhRBCHLWhtAh2SoOdCy+8sN/7+++/n0cffZQ333wzGezY7Xby8vIGPP+FF15g27ZtvPjii+Tm5nLKKadw3333cccdd3D33Xcfs6GZT0zTYOXKRKBTWQl9JXhud+L9tm2wahWMHXtch7R0Xeell15i9erV3HDDDbS1teFwOPjd736X/Iz++Mc/omkav/vd75KlgitWrCAtLY21a9cyZ84cfvGLX3DnnXdy8cUXA/DYY4+xevXqQ953586d/PWvf2XNmjXMnj0bgFGjRiX39w155eTkkJaWBiR6gn70ox/x4osvMmPGjOQ5r7/+Or/5zW+YNWsWjz76KGVlZTz00EMAjB07ls2bN/PjH//4GH5qQgghjugIKRpDZRHsIZOzE4/HefrppwkEAskvOYAnn3ySP/7xj+Tl5XHhhRfyve99L9m7s379eiZOnEhubm7y+Llz53LdddexdetWpkyZMuC9wuEw4XA4+d7n8x2fh6qrg+3bEz06B8w1gKJAUVGi56euDkpLj/ntn332WZxOJ9FoFE3T+MpXvsLdd9/N0qVLmThxYr9g8P3336empgaXq3/XYigUora2Fq/XS1NTE9OnT0/uMxqNnHrqqQcNZfV57733MBgMzJo166jbXFNTQ29vL+eff36/7ZFIJPn7rKqq6tcOoN/fGSGEEIOgqgqeeQbefTcxYuFwwNSpsGjRoI1YHK2UBzubN29mxowZhEIhnE4nK1eupLKyEoCvfOUrjBgxgoKCAj744APuuOMOduzYwd///ncAmpub+wU6QPJ9c3PzIe+5bNky7rnnnuP0RPvx+yEUSvwFGIjDAQ0NieOOg3POOYdHH30Us9lMQUEBRuNHv27HAW3q6elh2rRpPPnkkwddJzs7+xPdv29Y6uPo6ekB4N///jeFhYX99lkslk/UDiGEEMdYVRXccw9s2ZLo3emzc2di2w9+MKQCnpQHO2PHjuW9997D6/Xyt7/9jSVLlrBu3ToqKyu59tprk8dNnDiR/Px8zjvvPGpraykrK/vE97zzzju55ZZbku99Ph/FxcWf6jkG5HKB1ZqIeN3ug/cHAon9ruOTqOVwOCgvLz+qY6dOncpf/vIXcnJycA/UViA/P58NGzZw1llnARCLxdi4cSNTp04d8PiJEyeiaRrr1q1LDmPtr69nKR6PJ7dVVlZisVioq6s7ZI9QRUUF//znP/tte/PNN4/8kEIIIY6apukD59toGvzmN/D222CxgMcDJhNEo+D1Jrb/7//CQw8d96rjo5XyVvTNATNt2jSWLVvG5MmT+eUvfzngsX1DFzU1NQDk5eXR0tLS75i+94fK84FED0FfBVjf67goKYFx4xKJyAcO9eg67NuXiHxLSo7P/T+GxYsXk5WVxRe+8AVee+01du/ezdq1a7nxxhvZt28fAN/+9rd54IEHWLVqFdu3b+db3/rWYefIKS0tZcmSJXzta19j1apVyWv+9a9/BWDEiBEoisKzzz5LW1sbPT09uFwubrvtNm6++WaeeOIJamtreffdd/nVr37FE088AcA3v/lNqquruf3229mxYwdPPfUUjz/++PH+iIQQ4qRR0+rn0bW1/HzNTpa/VM3P1+zk0bW11LT6Yc8eWLcODAbIzk4EPKqa+Jmdnfjz2rWJ44aIlAc7B9I0rV8+zf7ee+89INHDAIk8jc2bN9Pa2po8Zs2aNbjd7uRQWEqpKlx0EWRlJZKRvV6IxRI/t21LbF+4cEhEvna7nVdffZWSkhIuvvhiKioquPrqqwmFQslg8NZbb+Xyyy9nyZIlzJgxA5fLxUUXXXTY6z766KNccsklfOtb32LcuHFcc801BAIBAAoLC7nnnnv47ne/S25uLtdffz0A9913H9/73vdYtmwZFRUVzJs3j3//+9+MHDkSgJKSEp555hlWrVrF5MmTeeyxx4ZO9Z0QQpzgalr9rHhjD1savaTZTYzKcpJmN7Gl0cuKN/bQ8Nb70NkJ6ekD56NmZCT279yZmgcYgKIfKrt0ENx5553Mnz+fkpIS/H4/Tz31FD/+8Y9ZvXo1o0aN4qmnnuKCCy4gMzOTDz74gJtvvpmioiLWrVsHJIY/TjnlFAoKCnjwwQdpbm7m8ssv5+tf//rH+vLz+Xx4PB68Xu9BvTyhUIjdu3czcuRIrFbrJ3vQqqpEVdb27YkcHqs10aOzcOGQGtM8GRyT36cQQgxTmqbz6NpatjR6+61YDonK3urWHi5oeJ/PPXIPSl4eDJSb2dsLLS2Joa55845rew/3/b2/lObstLa2csUVV9DU1ITH42HSpEmsXr2a888/n/r6el588UV+8YtfEAgEKC4uZtGiRdx1113J8w0GA88++yzXXXcdM2bMwOFwsGTJkn7z8gwJFRWJ8vJBnkFZCCGE+DgauoNHXLH8/c4c5ro9mFtbITMTjMbEEJaiJFI0uroSvTtjxqToKQ6W0mDn97///SH3FRcXJ3twDmfEiBE899xzx7JZx4eqHpfyciGEEOJY+WjF8oGraW1mA8HeXmJWO+bduxLzyFks4HQmEpUjEYjH4eyzh9R3nnQtCCGEEAI48orljtqdnPfS0yguJxQWJtIy4nHo6IC9exN5qaefDtdeO6RGL1Jeei6EEEKIoaFvxfItjV6cFmP/nJ14nIK1q8mN+LHO+kwiwKmqgqamRI9OKASjRsH3vjfk8lEl2DlKKczjFseQ/B6FEOLQDrdiebhmF2e31pFZUYaiqoky86ysRIVxOJx4RaOHnkg3hYZOH9MQZTAYgMRyBeLE1/d77Pu9CiGE6O+QK5a7VUa7jaRnZ6DrOt5glLaeMA26mTa7B296NnoofNxWBfg0pGfnCIxGI3a7nba2NkwmE+oQGoMUH4+mabS1tWG32/stnSGEEKK/AVcs7/agrnPR1dZJddBAszeINxglGtcxGRRyCVOiR7GGFUpT/QAHkP/jH4GiKOTn57N792727t2b6uaIT0lVVUpKSg4qqRRCCNHfQSuWp42gvWgkTWvXsy+zmN5oHE3XsRhVYnENa2sT75dVsnlvnCtL/JTnHJ+lkD4JCXaOgtlsZvTo0TKUNQyYzWbpnRNCiE9AQ+GF0TMofHMLBY272efIRHE4sER6yexqpc3h5q3JZxLojfLC1hZGZTkTa2kNARLsHCVVVWXGXSGEECethu4g79jzaLzwq2S++Dyl7XVYAp1ETWZ2l4zjvxNnUuMpZKLVSE1rDw3dwf49QykkwY4QQgghjqhvwsH2kjJWn3MZo8Nd2MNBQhY77Rm5xBWFWG8Eg6rQG4kROMRcPakgwY4QQgghjqhvwkFN0zEYjTTacrEYP6psjcbiGFWVuKZjMRpwmIdOiCHJC0IIIYQ4or4JB32hGOk2Ez2hWHLuMl3X6QnFSLeb8IdilOc4KUwbeMmJVBg6YZcQQgghhgxN0/uXnqfZkhMOBiIxDKpCR08Yi8lAOKphNKoYVZVMp4U543OHTHIySLAjhBBCiAPUtPpZvaWF2rYeQrE4VqOBsmwncyfkctXMUlZvaWFTfRd1nb34QzHsZgPF6TamlqQzZ3zukCo7Bwl2hBBCCLGfmlY/K97YQ2cgQr7Hit1sozcSY0ujl0ZvkKtmlnLd2WU0dAfxh6L0hGM4rUZcFhOFabYh1aPTR4IdIYQQQgCJoavVW1roDEQYneNMTsDqsppwWoxUt/bwwtYWvjnLOWTKyo+GJCgLIYQQAkjMpVPbllgA9MCZ5hVFId9jTc6hcyKRYEcIIYQQwEdz6dgPUTZuMxsIx+JDag6doyHBjhBCCCGAj+bS6T1EMBOMxIfcHDpHQ4IdIYQQQgAfzaXT5A0l59Dpo+s6Td7QkJtD52hIsCOEEEIIILHS+dwJuWQ4zFS39uAPRYlpGv5QlOrWHjIc5iE3h87ROLH6oYQQQghxXJXnuBJz6XzQRGdVDZGAH8XhYmJlOXMm5g+5OXSOhgQ7QgghhOinvGMfozasJPjBFuLBIAabDZtvAmrBRZBTkermfWwS7AghhBDiI1VVsHw5alsbDo8H0lwQi8Gmd2FfPdx4I1ScWAGPBDtCCCGESNA0WLkSdu2CaBSqqxOBjtEImZng98OqVTB2LKgnTtqvBDtCCCGESKirgw0boKkpEeR4PGAyJQKf5uZE0PPmm4njSktT3dqjduKEZUIIIYQ4vrzej3p1srPBYkn04FgsiffRaGK/15vqln4sEuwIIYQQIsHvh0AAbDY4YLkIFAWs1sR+vz817fuEJNgRQgghRILLBQ4HBINwwKSC6Hpiu8OROO4EIsGOEEIIIRI8Hhg1KpGn09YGoVAiaTkUSrw3mxP7PZ5Ut/RjkQRlIYQQQiSUlMD06YngJhqFjo7EkJXRCHl5iSDojDMSx51AJNgRQgghRIKqwkUXQX19oidn5EgwGCAeTyQlZ2fDwoUnVNk5yDCWEEIIIfZXUZGYOHDq1ETvTnd34ue0aSfkhIIgPTtCCCGEOFBFRWLiwLq6xDCWy5UYujrBenT6SLAjhBBCiIOp6gk1ceDhpDREe/TRR5k0aRJutxu3282MGTN4/vnnk/tDoRBLly4lMzMTp9PJokWLaGlp6XeNuro6FixYgN1uJycnh9tvv51YLDbYjyKEEEKIISqlwU5RUREPPPAAGzdu5J133uHcc8/lC1/4Alu3bgXg5ptv5l//+hdPP/0069ato7GxkYsvvjh5fjweZ8GCBUQiEf773//yxBNP8Pjjj/P9738/VY8khBBCnHg0Dfbsgc2bEz81LdUtOqYUXT9w1qDUysjI4Cc/+QmXXHIJ2dnZPPXUU1xyySUAbN++nYqKCtavX88ZZ5zB888/z+c+9zkaGxvJzc0F4LHHHuOOO+6gra0Ns9l8VPf0+Xx4PB68Xi9ut/u4PZsQQggx5FRVJRb/3L49UXJutcK4cYmqrCGejHy0399DJtMoHo/z5z//mUAgwIwZM9i4cSPRaJTZs2cnjxk3bhwlJSWsX78egPXr1zNx4sRkoAMwd+5cfD5fsndoIOFwGJ/P1+8lhBBCnHSqqmD5cti0CbKyEknJWVmJ98uXJ/YPAykPdjZv3ozT6cRisfDNb36TlStXUllZSXNzM2azmbS0tH7H5+bm0tzcDEBzc3O/QKdvf9++Q1m2bBkejyf5Ki4uPrYPJYQQQgx1mpbo0Wlvh8pKcLsTc+q43Yn37e2watWwGNJKebAzduxY3nvvPTZs2MB1113HkiVL2LZt23G955133onX602+6uvrj+v9hBBCiCGnri4xdFVcPPCin0VFiZ6durrUtO8YSnnpudlspry8HIBp06bx9ttv88tf/pIvfelLRCIRuru7+/XutLS0kJeXB0BeXh5vvfVWv+v1VWv1HTMQi8WCxWI5xk8ihBBCnED8/kSOjsMx8H6HAxoaTrgVzgeS8p6dA2maRjgcZtq0aZhMJl566aXkvh07dlBXV8eMGTMAmDFjBps3b6a1tTV5zJo1a3C73VRWVg5624UQQogThsuVSEYOBAbeHwgk9p9gK5wPJKU9O3feeSfz58+npKQEv9/PU089xdq1a1m9ejUej4err76aW265hYyMDNxuNzfccAMzZszgjDPOAGDOnDlUVlZy+eWX8+CDD9Lc3Mxdd93F0qVLpedGCCGEOJySkkTV1aZNiRyd/YeydB327UssGXGCLfo5kJQGO62trVxxxRU0NTXh8XiYNGkSq1ev5vzzzwfg5z//OaqqsmjRIsLhMHPnzuWRRx5Jnm8wGHj22We57rrrmDFjBg6HgyVLlnDvvfem6pGEEEKIE8P+i35u25bI0XE4Ej06+/YlqrJOwEU/BzLk5tlJBZlnRwghxElroHl2KioSgc4wmWcn5QnKQgghhEihYbbo50Ak2BFCCCFOdsNo0c+BDJ+wTQghhBBiABLsCCGEEGJYk2BHCCGEEMOaBDtCCCGEGNYk2BFCCCHEsCbBjhBCCCGGNSk9F0IIIU5ymqbT0B0kEInhMBspTLOhqsqRTzxBSLAjhBBCnMRqWv2s3tJCbVsPoVgcq9FAWbaTuRNyKc858RcBBQl2hBBCiGHvUD03Na1+Vryxh85AhHyPFbvZRm8kxpZGL43eIFfNLB0WAY8EO0IIIcQwdqiem/Mrc1mzrYXOQITROU6UD1c9d1lNOC1Gqlt7eGFrC6OynCf8kJYEO0IIIcQwdbiem50tfgKRGCUZ9mSg00dRFPI9Vmpae2joDlKcYU/RExwbUo0lhBBCDEOaprN6y4c9N1l2CrtbyNm7k8LuFkZn2ekIhKnv7MVmMgx4vs1sIByLE4jEBrnlx5707AghhBDDUEN3kNq2Hib6Gpj08loy6ndhDIeJWSx0Fo8iPvFM/hnx0OoPUZB2cM9NMBLHYjTgMJ/4ocKJ/wRCCCGEOEggEiNtbw2fWfcMdn8X/qx8otk2TKEgOTXbmN3SyPaJF9DktZPvsfUbytJ1nSZviImFHgrTbCl8imNDhrGEEEKIYchhVJn27jrM3R10lJQTcTjRDQYiDicdJeVYuju5oHYDWXYT1a09+ENRYpqGPxSlurWHDIeZOeNzT/jkZJCeHSGEEGJYKvS1Eejcxz53Fo4D4xUFGl1ZjPc2MmW0mef9NmrbemjxhbAYDUws9DBnvMyzI4QQQoghTA30UGiFRrOTjkAEl8WI0aASi2v4wzHsTieF0RAuK1w3rUxmUBZCCCHECcblwpXmYordRHXQQFcgQiwcw6iq5LqsjLbGcQWd4HKhqsoJX15+OBLsCCGEEMNRSQmMG0f6pk2cVlGBLxwnGtcwGVTcFgNKVRVMnZo4bpiTBGUhhBBiOFJVuOgiyMpCqarCE+kly2rAE+lNBDpZWbBwYeK4YW74P6EQQghxsqqogBtvhClToKMDdu5M/Jw6NbG9oiLVLRwUMowlhBBCDGcVFTB2LNTVgd8PLldi6Ook6NHpI8GOEEIIMdypKpSWproVKXPyhHVCCCGEOClJsCOEEEKIYU2GsYQQQojhQtNO6tycQ5FgRwghhBgOqqpg5UrYvh1CIbBaYdy4RPn5SVJ1dSgS7AghhBAnuqoqWL4c2tuhuBgcDggEYNMmqK8/qcrMByJ9W0IIIcSJTNMSPTrt7VBZCW43GAyJn5WVie2rViWOO0lJsCOEEEKcyOrqEkNXxcWgHLB4p6JAUVGi56euLjXtGwIk2BFCCCFOZH5/IkfH4Rh4v8OR2O/3D267hpCUBjvLli3jtNNOw+VykZOTw8KFC9mxY0e/Y84++2wURen3+uY3v9nvmLq6OhYsWIDdbicnJ4fbb7+dWCw2mI8ihBBCpIbLlUhGDgTQdR1vMEp7TxhvMIqu64ncHas1cdxJKqUJyuvWrWPp0qWcdtppxGIx/ud//oc5c+awbds2HPtFqNdccw333ntv8r3d/tEy9PF4nAULFpCXl8d///tfmpqauOKKKzCZTPzoRz8a1OcRQgghBt2Hq5v7179FVXoxXb1RYpqGUVVJt5uo6KrH9ZnpJ8Xq5oeS0mDnP//5T7/3jz/+ODk5OWzcuJGzzjorud1ut5OXlzfgNV544QW2bdvGiy++SG5uLqeccgr33Xcfd9xxB3fffTdms/m4PoMQQgiRUqrK3rPm0LzuPYzbq/DkFaA7HCiBAIa6RralZ5J35vmMOInn2xlST+71egHIyMjot/3JJ58kKyuLCRMmcOedd9Lb25vct379eiZOnEhubm5y29y5c/H5fGzdunVwGi6EEEKkiKbpPBtJ4z/nXkrv+Im4gz4yGvfgDvronTCJ/5z7Rf4dTUPT9FQ3NWWGzDw7mqZx0003MXPmTCZMmJDc/pWvfIURI0ZQUFDABx98wB133MGOHTv4+9//DkBzc3O/QAdIvm9ubh7wXuFwmHA4nHzv8/mO9eMIIYQQg6KhO0htWw9plRW8c8oE3K2NmIIBojYHvpwClEicmtYeGrqDFGfYj3zBYWjIBDtLly5ly5YtvP766/22X3vttck/T5w4kfz8fM477zxqa2spKyv7RPdatmwZ99xzz6dqrxBCCDEUBCIxQrE4drMNVAVfXlG//TYztPhCBCInb+HOkBjGuv7663n22Wd55ZVXKCoqOuyx06dPB6CmpgaAvLw8Wlpa+h3T9/5QeT533nknXq83+aqvr/+0jyCEEEKkhMNsxGo00HuIYCYYiWMxGnCYh0z/xqBLabCj6zrXX389K1eu5OWXX2bkyJFHPOe9994DID8/H4AZM2awefNmWltbk8esWbMGt9tNZWXlgNewWCy43e5+LyGEEGKo0jSd+s5etjf7qO/s7Zd/U5hmoyzbSZM3lCg134+u6zR5Q5TnOClMsw12s4eMlIZ5S5cu5amnnuIf//gHLpcrmWPj8Xiw2WzU1tby1FNPccEFF5CZmckHH3zAzTffzFlnncWkSZMAmDNnDpWVlVx++eU8+OCDNDc3c9ddd7F06VIsFksqH08IIYT41Gpa/aze0kJtWw+hWByr0cCobAeTi9PIdllwmI2cPz6HRm+Q6tYe8j1WbGYDwUicJm+IDIeZOeNzUVXlyDcbphT9wDBwMG9+4LTWH1qxYgVXXnkl9fX1fPWrX2XLli0EAgGKi4u56KKLuOuuu/r1xuzdu5frrruOtWvX4nA4WLJkCQ888ABG49HFcj6fD4/Hg9frlV4eIYQQQ0ZNq58Vb+yhMxAh32PFbjbS2N3LlgYf0bhGcYadLKeFsmwn4/JdbG/yU9vWQziWGLoqz3EyZ3wu5TnDc0LBo/3+TmmwM1RIsCOEEGKo0TSdR9fWsqXRy+gcJ4qi0BkI8159N73hGDEN8j1WKvJdNPvCZDjMLJlRis1sIBCJ4TAbKUyzDesenaP9/j55s5WEEEKIIayvpDzfY0VRFHRdp7Y1QDASJ8tuwtPehNreg0ctxFVcTHV7Ly9WtfDNWWXDOsD5JCTYEUIIIYagfiXlgD8Uo7M3wrjufcx87XXym/dCMIj7LRe9o0ZjPfVsakyGk3o+nUORYEcIIYQYgvYvKXdZTUTiGgVNu/n8+pW4Aj5a3dkE3NlYbJBTs43PtDTSPusSApFRqW76kDMk5tkRQgghRH8HlpSbFThzyxs4/N3syyvFa7JhsZjB7aajpBxzdydTN72Kwyhf7QeST0QIIYQYglRVYe6EXDIcZqpbe/C0NVLWUc8+Zxa9UQ2jQSXdYQYUUKDRlUV5Rz2FvrZUN33IkWBHCCGEGKLKc1xcNbOUCQUeot0+LLEIYbMVVYFMhwmLUSUSi9MRiKA6nRTaFNRAT6qbPeRIzo4QQggxhJXnuBh1tpPmjCiOt3IocjppiJvo6o3S3RvBqKrkuqyMtsZxBZ3gGp5z6nwaEuwIIYQQQ5yKToHbAvnZeGpqKJg2DV9EIxrXMBlU3BYDSlUVTJ0KJSWpbu6QI8GOEEIIMZRVVcHKlbB9O7S2wq5dKHV1eKZNg+JiCARg1z7IyoKFC0GVDJUDSbAjhBBCDFVVVbB8ObS3JwKbESMgNxc2boT166GlBXJyEj06CxdCRUWqWzwkSbAjhBBCDEWalujRaW+HykroW09y5MhE0PPOOzB6NHz721BaKj06hyGfjBBCCDEU1dUlhq6Kiz8KdPqoKowdC11diT9LoHNY8ukIIYQQQ5HfD6EQOBwD73c4Evv9/sFt1wlIgh0hhBBiKHK5wGpNJCAPJBBI7JdS8yOSYEcIIYQYikpKYNw4qK8HXe+/T9dh375EQrKUmh+RBDtCCCHEUKSqcNFFiZLybdvA64VYLPFz2zYpNf8Y5BMSQgghhqqKCrjxRpgyBTo6YOfOxM+pUxPbpdT8qEjpuRBCCDGUVVQkKq/q6hLJyC5XYuhKenSOmgQ7QgghxFCnqom5dMQnImGhEEIIIYY1CXaEEEIIMaxJsCOEEEKIYU2CHSGEEEIMaxLsCCGEEGJYk2BHCCGEEMOaBDtCCCGEGNYk2BFCCCHEsCaTCgohhBAppGk6Dd1BApEYDrORwjQbqqqkulnDigQ7QgghRIrUtPpZ/UETnVU1KAE/usNFRkU5cyflU57jSnXzhg0JdoQQQogUqGn18+xfXqb0tRf4bHs91liEkNHM7teKefbMOXzuS+dKwHOMSLAjhBBCDDJN03nr328wddUfyIsE8Gfn02W1YQoFqWyqJWPVH3jbZWHUFXNlSOsYkARlIYQQYpA1dAbw/OdZ8rtbCbrTUXQNXVWJOJx0jCgnK+THtfo5GjoDqW7qsCA9O0IIIcQg019+iYlvrsGux0hvb0IzGAm60+kqGUXQk0EgJ5/s+loiu3dD1sRUN/eEJ8GOEEIIMZiqqsh86gki/m4CWTnoZguGeAxnZxuWXj/N4ybjszpxx6M4wsFUt3ZYSOkw1rJlyzjttNNwuVzk5OSwcOFCduzY0e+YUCjE0qVLyczMxOl0smjRIlpaWvodU1dXx4IFC7Db7eTk5HD77bcTi8UG81GEEEKII9M0WLkSWzhIPC2NiAaoKnGTmV5POqZQiPT6WiJeH1aXg5yC7FS3eFhIabCzbt06li5dyptvvsmaNWuIRqPMmTOHQOCjMcqbb76Zf/3rXzz99NOsW7eOxsZGLr744uT+eDzOggULiEQi/Pe//+WJJ57g8ccf5/vf/34qHkkIIYQ4tLo62L4dddw47IV5OMK9BCMx4pqOrij02hyoHR0Ute0j67TJqKUjUt3iYUHRdV1PdSP6tLW1kZOTw7p16zjrrLPwer1kZ2fz1FNPcckllwCwfft2KioqWL9+PWeccQbPP/88n/vc52hsbCQ3NxeAxx57jDvuuIO2tjbMZvMR7+vz+fB4PHi9Xtxu93F9RiGEECexzZvhvvtg7Fjo7CT0xn/p7fLjM9uJqgZM8SiZ3nb0z3wG9wP3Q0VFqls8pB3t9/eQqsbyer0AZGRkALBx40ai0SizZ89OHjNu3DhKSkpYv349AOvXr2fixInJQAdg7ty5+Hw+tm7dOoitF0IIIY7A5QKrFQIByM7GOvMzpJeNoMCsU0KQAjWKsygf9w3fkkDnGBoyCcqapnHTTTcxc+ZMJkyYAEBzczNms5m0tLR+x+bm5tLc3Jw8Zv9Ap29/376BhMNhwuFw8r3P5ztWjyGEEEIcWkkJjBsHmzZBZSVkZ6NkZWH2eiEUSgxzffazcO65qW7psDJkenaWLl3Kli1b+POf/3zc77Vs2TI8Hk/yVVxcfNzvKYQQQqCqcNFFkJUF27aB1wvxOCgKdHTAiBGJ/eqQ+XoeFobEp3n99dfz7LPP8sorr1BUVJTcnpeXRyQSobu7u9/xLS0t5OXlJY85sDqr733fMQe688478Xq9yVd9ff0xfBohhBDiMCoq4MYbYcqURICzc2fi59Spie0yfHXMpXQYS9d1brjhBlauXMnatWsZOXJkv/3Tpk3DZDLx0ksvsWjRIgB27NhBXV0dM2bMAGDGjBncf//9tLa2kpOTA8CaNWtwu91UVlYOeF+LxYLFYjmOTyaEEEIcRkVFIkm5rg78/kQuT0mJ9OgcJykNdpYuXcpTTz3FP/7xD1wuVzLHxuPxYLPZ8Hg8XH311dxyyy1kZGTgdru54YYbmDFjBmeccQYAc+bMobKykssvv5wHH3yQ5uZm7rrrLpYuXSoBjRBCiKFLVaG0NNWtOCmktPRcUQZe3GzFihVceeWVQGJSwVtvvZU//elPhMNh5s6dyyOPPNJviGrv3r1cd911rF27FofDwZIlS3jggQcwGo8ulpPScyGEEOLEc7Tf30Nqnp1UkWBHCCGEOPEct3l2lixZwquvvvqpGieEEEIIMVg+drDj9XqZPXs2o0eP5kc/+hENDQ3Ho11CCCGEEMfExw52Vq1aRUNDA9dddx1/+ctfKC0tZf78+fztb38jGo0ejzYKIYQQQnxin6jGLTs7m1tuuYX333+fDRs2UF5ezuWXX05BQQE333wz1dXVx7qdQgghhBCfyKcq6G9qamLNmjWsWbMGg8HABRdcwObNm6msrOTnP//5sWqjEEIIIcQn9rGDnWg0yjPPPMPnPvc5RowYwdNPP81NN91EY2MjTzzxBC+++CJ//etfuffee49He4UQQgghPpaPPalgfn4+mqbx5S9/mbfeeotTTjnloGPOOeecgxbvFEIIIcRHNE2noTtIIBLDYTZSmGZDVQeef058Oh872Pn5z3/OF7/4RaxW6yGPSUtLY/fu3Z+qYUIIIcRwVdPqZ/WWFmrbegjF4liNBsqyncydkEt5jivVzRt2Pnawc/nllx+PdgghhBAnhZpWPyve2ENnIEK+x4rdbKM3EmNLo5dGb5CrZpZKwHOMpXRtLCGEEGIoOl5DTJqms3pLC52BCKNznMllk1xWE06LkerWHl7Y2sKoLKcMaR1DEuwIIYQQ+znaIaZPEhA1dAepbesh32M9aH1IRVHI91ipae2hoTtIcYb9uDzfyUiCHSGEEOJDRzvE9ElzbgKRGKFYHLvZNuB+m9lAiy9EIBI7Xo94UpJgRwghhODoh5g0DZ5Yv19AZLRgaqinc9cOVlZ7uOgLMyjP8wx4D4fZiNVooDcSw2U1HbQ/GIljMRpwmOXr+ViST1MIIYTg6IaYqlv8dPdGkgFRZv0uyt5YQ0b9LgzhEF2agfa31zDq5qtRx1cedI/CNBtl2U62NHpxWoz97qPrOk3eEBMLPRSmDdzzIz6ZTzWDshBCCDFcfDTENHA/gM1soDsYSQZEmXtrOO3JRyh6fwNx1UhX4Uj0zExsW94n8NOfQVXVQddQVYW5E3LJcJipbu3BH4oS0zT8oSjVrT1kOMzMGZ8rycnHmAQ7QgghBP2HmAYSjMRRFZW4DkWNuznrsR9RuGUjzvYWcqu3kF/1HhYtxr78kejt7bBqFWjaQdcpz3Fx1cxSJhR46O6Nsqc9QHdvlImFHik7P05kGEsIIYTg6IaYynOcULWNU/+5gox9ewi604ha7RjiMZydbRh7fPSOmgBlxYmenbo6KC096F7lOS5Gne2UGZQHiQQ7QgghBB8NMTV6g1S3JoaqbGYDveEYu9oDOCxGZo5Kx/TMGxg72olarMRsDlAU4qqZXk86hs4ORrTX4zq1DDpawO8/7P2kvHxwyDCWEEII8aEDh5g27/OyYXcX7f4wPaEY69a8i313Dd1ZeYRQ0SMRdCAS0+iJxAnbHWSHfCjNzWC1gkuGpIYC6dkRQggh9tM3xPRGbTt/eqsORYFRWU4cFiPOnY3EAr1480cQScvA0t5Ke8yNpoOqKBgMBgKBHuK1e3DMOx9KSlL9OALp2RFCCCEG9EG9F12HyUVpuG0mDKqCKc2D1eXEFA7SXjyKuNVGZq+PdINOhs2IKxaGQICdup29Z54PqnzNDgXyWxBCCCEOcKg5d3w5BXSVjCLf2051zMLO0kriubk44hFsvi7sAR++EWX8c/4V/DuahqbpKXwK0UeGsYQQQogDHHJZB1Wldub5VDQ2kN+wC7W4mKaKKTg623C1NxFMy+Sty76Bklcqa1wNIdKzI4QQQhzgcHPudJaU8dL5l7KzYDRpQT/pjXswaDH2TT6Dt75yHZ2lo7GZDYRjcVnjaoiQnh0hhBDiAP3m3DGpeNqaMAUDRG0OvNn5bE8von3eFYScITL0CFGbA19OQTJHR9a4GlrktyCEEEIcoG/OnejWrZT+8wVGttdjiUUIG83szipG/ewcfGXl7PCF+i0aCrLG1VAkw1hCCCHEAMo79nHlxn8yobmWLqubXRmFdFndTGip5cp3/8mSjKCscXWCkJ4dIYQQ4kCaBitXkhbw4Tn7dLLDcaJxDZNBxW0ZhVJVRdpra7jqqm+xelsbtW09tPhCWIwGJhZ6mDM+V9a4GkIk2BFCCCEOVFcH27dDcTGKquKxHTAQUlQEVVWUh7oYdXaZrHE1xEmwI4QQQhzI64WOjsSSD5oGHg/sl5eDwwENDeD3yxpXJwAJdoQQQpwUNE0/uh6Yqir44x8TP6urwWaDrCwYNw6ysxPHBAKy9tUJRIIdIYQQw15Nq5/VW1qobeshFItjNRooy3Yyd8JHuTWaptOyYRPWxx7G0tWBLT8fpbMzEew0NSV6e6ZPTwQ++/bB1Kmy9tUJQoIdIYQQw1pNq58Vb+yhMxAh32PFbrbRG4mxpdFLozfIVTNLAVj9QROlv1tB3u69tBeVkZ/lZEygF6vPl+jB8XrhvfcgPz/Rw7Nwoax9dYKQYEcIIcSwpWk6q7e00BmI9JsPx2U14bQYqW7t4U8b6ghGNZS9e/hs616ihUVYzQbqdDuB/LFM7mnC7utO5O40NcHMmXDVVVBRkdqHE0ctpSHpq6++yoUXXkhBQQGKorBq1ap++6+88koURen3mjdvXr9jOjs7Wbx4MW63m7S0NK6++mp6enoG8SmEEEIMVYda0BNAURTy3BbW7+qkobuXsdY4rh4vplAQVyhApt1Eh83N1pGT0M8+G84+OxHgLF4sgc4JJqU9O4FAgMmTJ/O1r32Niy++eMBj5s2bx4oVK5LvLRZLv/2LFy+mqamJNWvWEI1Gueqqq7j22mt56qmnjmvbhRBCDH2HXNDzQzFNxxuMcGaslYo3nyOjfhdpDXuJWawE3ekYC0rpVFV8+Zl4VBUyMxOVWeKEktJgZ/78+cyfP/+wx1gsFvLy8gbcV1VVxX/+8x/efvttTj31VAB+9atfccEFF/DTn/6UgoKCY95mIYQQJ479F/R0WU0H7feHYoxo2ct5VavxBLoJZGRj9XuJWaw4O9swB/z0jqggGkuTpOQT2JDPrFq7di05OTmMHTuW6667jo6OjuS+9evXk5aWlgx0AGbPno2qqmzYsOGQ1wyHw/h8vn4vIYQQw0/fgp5N3hC6rvfbp+s63T0h5la/icPXRceI0bSVVRC12rD09hC2OzCGeimur8ZevT1RhSVJySekIf0bmzdvHn/4wx946aWX+PGPf8y6deuYP38+8XgcgObmZnJycvqdYzQaycjIoLm5+ZDXXbZsGR6PJ/kqLi4+rs8hhBAiNfoW9DzUGlaVsW5O6W2myZMFCgQ9GTSPm0wgIxtjJEw8GiPT14l17Bi48UbJ1TlBDelqrMsuuyz554kTJzJp0iTKyspYu3Yt55133ie+7p133sktt9ySfO/z+STgEUKIYao8x8VVM0uT8+zsv4bV55Qo6U4DHWYnHYEILosRzZ2Od+wpxLq6cekRxus9qF+VpOQT2ZAOdg40atQosrKyqKmp4bzzziMvL4/W1tZ+x8RiMTo7Ow+Z5wOJPKADE52FEEIMX+U5Lkad7Tx4BuU6I6S5mGI3UR000BWIEAvHMKoqGXnZjLbGcQT9kpR8gjuhgp19+/bR0dFBfn4+ADNmzKC7u5uNGzcybdo0AF5++WU0TWP69OmpbKoQQoghZsA1rEpKYNw40jdt4rSKCnz9Vjc3oFRVSVLyMJDSYKenp4eamprk+927d/Pee++RkZFBRkYG99xzD4sWLSIvL4/a2lq+853vUF5ezty5cwGoqKhg3rx5XHPNNTz22GNEo1Guv/56LrvsMqnEEkIIcWSqChddBPX1KFVVeIqKEot8BgKwa58kJQ8Tin5gevogWrt2Leecc85B25csWcKjjz7KwoUL2bRpE93d3RQUFDBnzhzuu+8+cnNzk8d2dnZy/fXX869//QtVVVm0aBHLly/H6XQedTt8Ph8ejwev14vb7T4mzyaEEOIEUlUFK1fC9u0QCiUW+ayoSAQ6kqszZB3t93dKg52hQoIdIYQ4CWga1NWB359Y66qkpH+PzZH2iyHnaL+/T6icHSGEEOITGajnZty4xBBWX8+NqkJpaUqbKY4PCXaEEEIMb1VVsHw5tLdDcfFHOTmbNkF9vcyfcxKQ/jkhhBDDl6YlenTa26GyEtxuMBgSPysrE9tXrUocJ4YtCXaEEEIMX3V1iaGr4mI4YNVzFAWKihI9P3V1qWmfGBQS7AghhBi+/P5Ejo7DMfB+hyOx3+8f3HaJQSXBjhBCiOHL5UokIwcCA+8PBBL7Xa7BbZcYVBLsCCGEGJ40LfFKS0sMZR2Yl6PrsG9fIjlZZkge1qQaSwghxPCiafDyy/DPfyaCmUAAdu9O5OVMm5bI3wkEEvtkhuSTggQ7Qgghho+qKnj0Ufj739GDQaJ2B9GiEigfg23vHtT166GlBXJyEmteyQzJJwUJdoQQQgwPVVVwyy3w2mtooRCaoqB4/aitrfjTsqmdfiajAu04x46Fb387MYGg9OicFOS3LIQQ4sSnabBsWTLQiRiMhA1mYkYDJk0jvbOFtPfe5j1bDr6m1kSQI4HOSUN+00IIIU58u3bBmjXE4xpRRSWqGNBRiCsGwgYTiq6T29pANBiitdWL5vWlusViEEmwI4QQ4sT3xhtoXh8Bo4W4oqKioyigADoKUdWAIRqhqLORLk2lWTelusViEEmwI4QQ4oSnBQKJXh3VQNxgxLBfmbmigEZi9mSXr5uG/FJ8OfmpaqpIAQl2hBBCnLg0DfbsoTNuIGowYouGCJus6IqKIR5D0TXQdYzxGDrQlp7N9unn4rCaU91yMYikGksIIcSJqaoqscjn9u2YO73EDEbswR40HYJmC5ZYFEM8hiEWQ0GnzZ3FkwuuoWTKJArTbKluvRhEEuwIIYRIOU3TaegOEojEcJiNFKbZUFXl0CdUVcHy5YlVy4uL0XMK2NviZezmDVijYXRdJ6oa0FUDmknF53Dz0IKlRCvGM2d87uGvLYYdCXaEEEKkVE2rn9VbWqht6yEUi2M1GijLdjJ3Qi7lOQOsWaVpiR6d9nb0igp84TiRWBzv6PG8b7BQuf0djJEIcaORgMFKXXYJf56xkLazzueuc8oGvqYY1iTYEUIIkTI1rX5WvLGHzkCEfI8Vu9lGbyTGlkYvjd4gV80sPTg4qauD7dvpysyhem83XYEIMU0jrukEMgrpnOahvLOB2pmzqckpZUPOaNLTHNx1djljciXQORlJsCOEECIlNE1n9ZYWOgMRRuc4UZQPK6asJpwWI9WtPbywtYVRWc7+w05+P/5uP5t6rfRqUVwWIyaDkWhcI6bpeOM22g1W1maPoXPkWKYXph26l0icFKQaSwghREo0dAepbesh32NNBjp9FEUh32OlprWHhu5gv32aw0lDCLRAD5kOM2ajAUVRMBsNpNlMGIK9+DAStNhAB13XB/OxxBAkwY4QQoiUCERihGJx7GYjuq7jC0Zp7wnjC0bRdR2b2UA4FicQifU7r8GdTW1GEQW+dtgvjglGYzR7g2R1tbA3pwTPmHIK021sbfKx4o091LT6B/kJxVAhw1hCCCFSwmE2YjUaaOzupdkbprM3kXtjVFUy7GbyPBYsRgMOc/+vqkBMY+PUWRT628msq8GflUfUaiPU3kVhaxOh9Axeq5yJMxgl12igPNtBTVtg4CExcVKQYEcIIURKFKbZSLObWLOtBbNBwWUzJXNvWnxB6rt6Ob8y96A5cRxmI90jyvnvgi8z6Z21ZNTvwtraTE9Yp7ZkLC+UT2ebM5/0Ri+7TIFk4NQ3JFacYU/RE4tUkWBHCCFE6vQNQx2Qs5N4rzNQH0xhmo2ybCebo4WELr0GT1sTgY4uXm8Os9uWQW8cXBYD2U4LMU2n1R/CG4qQ6bAcNCQmTg4S7AghhEiJhu4g3cEop5Wm0+QN09UboSccw6iq5Lqt5LktdPVGD+qNUVWFuRNyafQGqW7vJT8tl6grm2pfE+FoHKfVSI7TikFVMahgdqi0+EKgg91kSOETi1SRYEcIIURK9CUoj8pyUpRuxx+KEYlrmA0qLquRuK6zpz0wYG9MeY6Lq2aWJicj7AxEiGs6JqOBXJcVm/nAoEZBR0Hqsk5OEuwIIYRIib4E5d5IDJfVhNtm6rc/GI4NmKDcpzzHxaiznTR0B9nS6KU3EqMnHCMYjWMwKJgMKtG4Rk8ohtNqJNNhJhiND8ajiSFGgh0hhBDHxZHWu+rLvdnS6MVpMaLoOu7WRkzBABGrnWrcTChOP+yinaqqJIe4itLtgH7QkFjOh0NioBwycBLDm/zWhRBCHHNHs97V/rk3/o3vM/vt58lp3IMei9NpcVJcOppx111+VKXi+wdOp45IoyccTw6JOS0GatoCTCz0yGrnJykJdoQQQhxTH2e9q/IcF98KbMfwxP1YWxqJqgaiZgvWtAwmmMI4n/w9ZDqgouKw99w/cKppC5DvsZJmNxGMxKlpC5DhMMtq5ycxCXaEEEIcMx97vautWyl88D5iDXsIKwbUaBRLOAQBH6FgDwrgWLUKxo4F9fCT/h+YtNziC2ExGphY6GHOeFkb62QmwY4QQoiP5XC5OB9nvaviNCs89BDxXbsI6yoRiwnFYMCg66jhENa2FroUI/F338ddVwelpUds2/5Jy4fKFRInHwl2hBBCHLUj5eJ8tN7VwLkxNrOBFl8oUU6+Zw/6f/9LLK4RsjsxGhPl4hqg2eyYg724OlvprGvC6fUd9WKO+yctCwEpXgj01Vdf5cILL6SgoABFUVi1alW//bqu8/3vf5/8/HxsNhuzZ8+murq63zGdnZ0sXrwYt9tNWloaV199NT09PYP4FEIIcXLoy8XZ0uglzW5iVJaTNLuJLY3e5EKb+5eTDyQYiX9UTr5zJ3Gvj4jBhPHAGXAUhZjZjCUSIhwI0qybBryeEEcjpcFOIBBg8uTJPPzwwwPuf/DBB1m+fDmPPfYYGzZswOFwMHfuXEKhUPKYxYsXs3XrVtasWcOzzz7Lq6++yrXXXjtYjyCEECeFA3NxXFYTBlXBZTUxOsdJZyDCC1tbyHdbKct20uQNoev9Axhd12nyhijPcSarojRDIiHZFIsedE8dBVWL05GRiy8nf1CeUwxPKR3Gmj9/PvPnzx9wn67r/OIXv+Cuu+7iC1/4AgB/+MMfyM3NZdWqVVx22WVUVVXxn//8h7fffptTTz0VgF/96ldccMEF/PSnP6WgoGDQnkUIIYazo83FafKFPlrKoTVxvM1sIBiJ0+QN9a+KGjMGPT0DPdxKXNcwhYLETWZ0VUWJx7H0+olarLx/5nw+ZzWn6MnFcJDSnp3D2b17N83NzcyePTu5zePxMH36dNavXw/A+vXrSUtLSwY6ALNnz0ZVVTZs2HDIa4fDYXw+X7+XEEKIQ/soF2fgfyPbzAbCsTiBSCxZFTWhwEN3b5Q97QG8PWE+Y/DzjfQA5b0doGlQWorp3HMwGI0ETVaiZjNqLIop2Isp1EvMaOb9STPRz50t8+OIT2XIJig3NzcDkJub2297bm5ucl9zczM5OTn99huNRjIyMpLHDGTZsmXcc889x7jFQggxfB24tMOB+uXi0L8qKrplKxlrnsOzpxYlHAKrFcaNg4suQv3mN1D31hN/9316YzHMRjOqrhEzGNlTNJq3vnQtn5uYL9VU4lMZssHO8XTnnXdyyy23JN/7fD6Ki4tT2CIhhBjaDlraYb+hrL5cnANnKFbRKX7ndfjlL8HrhTFjYMQY6O2FTZugvh5uvBH3sh8S+cOf8L7+Jl6fn6DJSkP5BPzzFvC5C2bK/DjiUxuywU5eXh4ALS0t5Od/lJjW0tLCKaeckjymtbW133mxWIzOzs7k+QOxWCxYLJZj32ghhBim9p+h+Ii5OABVVfDYY/DXv4LXi240Et9ZTaSomPiUaTgrKlCqqmDVKrjjDrLuv5uMPXtpbWzDZLGRNXIkhRkO6dERx8SQzdkZOXIkeXl5vPTSS8ltPp+PDRs2MGPGDABmzJhBd3c3GzduTB7z8ssvo2ka06dPH/Q2CyHEcDZQLk53b5SJhZ5+S0BQVQX33AN//zv09BB1Oukx2wj3htB37KTnhRfZ8v4uujNyEsfW1YGqoo4aSd5nT6fstIkU982wLMQxkNKenZ6eHmpqapLvd+/ezXvvvUdGRgYlJSXcdNNN/PCHP2T06NGMHDmS733vexQUFLBw4UIAKioqmDdvHtdccw2PPfYY0WiU66+/nssuu0wqsYQQ4jg44gzFmpYIcrZsAaORmNlCj2ZAAww2B+ZIEJevC2/1DjYZT+HUWA8uvz+lzySGv5QGO++88w7nnHNO8n1fHs2SJUt4/PHH+c53vkMgEODaa6+lu7ubz372s/znP//BarUmz3nyySe5/vrrOe+881BVlUWLFrF8+fJBfxYhhDhZHHaG4ro62LgR4nH0tDQi3X404qhGIygQN5kxRCNk+ztpb2+hwWJgjMM5dIcZxLCg6AfO+nQS8vl8eDwevF4vbrc71c0RQogT1+bNcOutsG8fXrub3l17sUZ6CRutKKqCCthjYSIOJ525xVRVnMrkX/2I4ixnqlsuTkBH+/0twbQQQohjx+UCp5NwLE5Hd4BOmxvNYMIWC2PQ4hCLEY/GUMNhQhmZvDvlLAIxLdWtFsOcBDtCCCGOnZIStKlT6YnoWAJ+4lYrnWnZBK02jPEYjkgviq6zJ28kay+6mu4R5cm5eYQ4XiTYEUIIceyoKi3nXcDegpHYtDjZ/k5iuo7PkUbYbKXX5mRb+SR+feF1vOXI77dOlhDHi4TTQgghPh5NSyQi+/2JYauSElA/+rezd2Q5zy68hgvW/4uC998io7sLXdfpcXrYNmYKz8+4kM32PKZZjP3n5hHiOJFgRwghxNGrqoKVK2H7dgj1X/qBigogsbRE94hynht7G4XdrRh3VdPYHWSHO48GTy6aopJhNHDZ6SUyO7IYFBLsCCGEODpVVbB8ObS3Q3ExOBwQCPRb+oGKiv5LS+QXoRQUY9F1RoZiFMTiNHQHOb00g5llWal+InGSkJwdIYQQR6ZpiR6d9naorAS3GwyGxM/KysT2VatA05JLS2Q4zFS39uAPRYnrOooCXb1RitLtzJ2QJ8NXYtBIsCOEEOLI6uoSQ1fFxaAcEKQoChQVfbT0Ax9jaQkhBoEMYwkhhDgyvz+Ro+NwDLzf4YCGhsRxHzri0hJCDBIJdoQQQhyZy5VIRg4EEkNXBwoEEvtd/XtsDru0hBCDRIaxhBBCHFlJSaLqqr4eDlxlSNdh375ENVZJSWraJ8RhSM+OEEKIhMPNn6OqifLy+nrYti2Ro9NXjbVvH2RlwcKF/ebbEWKokGBHCCFOIJqmH58cmKOYP4eKikR5ed9xDQ2J46ZOTQQ6fccJMcRIsCOEECeImlY/q7e0UNvWQygWx2o0UJbtZO6E3E9X3XSU8+cAiZ9jxx52BmUhhhoJdoQQ4gRQ0+pnxRt76AxEyPdYsZtt9EZibGn00ugNfvJy7v3mz9ErKvCF40SDMUwmG+6KCpSqqsT8OWPH9h/SKi09lo8nxHElwY4QQgxxmqazeksLnYEIo3OcKB/Oc+OymnBajFS39vDC1hZGZTk//pDWh/PndGXmUL23m65AhJimYVRV0h1mxmTkkNY3f44EOOIEJcGOEEIMcQ3dQWrbesj3WJOBTh9FUcj3WKlp7aGhO/jxy7z9fvzdfjb1WunVorgsRkwGI9G4Rqs/RE8ATov24Npv/hwhTjQyyCqEEENcIBIjFItjNw/871Ob2UA4FicQiX3sa2sOJw0h0AI9ZDrMmI0GFEXBbDSQ6TCj9fTQENTRHM5P+xhCpIwEO0IIMcQ5zEasRgO9hwhmgpE4FqMBxyGCocNpcGdTm1FEga8dDpg+Bx0K/O3UZBbT4M7+BC0XYmiQYEcIIYa4vlXEm7wh9AMm9NN1nSZviPIcJ4VptoNP1jTYswc2b0781LR+uwMxjY1TZxFJyySzrgZzwI8Sj2MO+MmsqyGcnsm7U84iENMOvrYQJwjJ2RFCiCGubxXxRm+Q6tZE7o7NbCAYidPkDZHhMDNnfO7ByclHMXeOw2yke0Q5/13wZSa9s5aM+l04O1qImy20lo/ng1Nn0Z1Z8ol6jYQYKuRvrxBCnAD6VhHvm2enxRfCYjQwsdDD7MocLEYD25t9H000uGP7Uc2d09drtDlaSOjSa/C0NWEKBojaHHiz86lu72XioXqNhDhBSLAjhBAniIFWEQ9G4qzZesBEg5l2vvTyn8lqb4fKSuir4HK7E++3bUvOnaOq6ke9Ru295KflYsv5sNeovffQvUZCnEAk2BFCiBPI/quI17T6eWL9Hrr8IcZGuvDEQniNVpr2Ban777sYxpWQfkCpOoqSWNdqv7lzDtdrNGf8p5ydWYghQIIdIYQ4AfVNNGjeuYMvb3+DzH27MYbDxCwWgg4Xls52antKmKbrB83Ng8ORWNdqv7lzBuo1OmbrbgmRYhLsCCHECaihO4j/vQ9YsPZp3AEv/qx8otk2TKEg6ft24e5oYld9Hb7CNDw2U/+TA4FEsrKrf4/N/r1GQgwnUnouhBAnkg9LyWObNjH1pVW4/N10lJQTcTjRDQYiDictoyegmUwU7qoiGj1gbh5dh337EtVYJSWpeQYhBpn07AghxBCjafrBw0no8PLL8M9/wr595Pl7cL2/jUBmNraMLIKejI8uoKo0jqwkf/t72D94DyZWflSNtW8fZGXBwoWyUrk4aUiwI4QQQ0hNqz+ZKNxXXXVqbzPz3/wX6a+sgd5ecLuxOhxEFB2Tt5u87e/TPG7yfgGPTqM7i/SiEWRXjIWOjkSOjtUKU6cmAp0P59kR4mQgwY4QQgwRO5v9PPxKDZ3+IOPDXZR1N5C+cxs5779FrL2BsMWAZeRIiMVQ2tpwRoIEPA60QC/uvbUEJqQR03T84RhpWoT0kYXw7W/T2BMh3NWNJT2NvAljUI2GVD+qEINKgh0hhBgCdrb4uO/ZKmJbt7Jo43OctuNtMn0dWKMh0EFDIez2oHnSUBwOLPn5GHw+cnq6aM8qwNLdSbijk6jTQ67TwriuVsKjT+HRPXFqO8KEYmasrWHKOnczd4KUk4uTiwQ7QgiRYjWtfh5+pZb45i3c9OLvGFO/A0s4SByFGCoGRccQj2PxdROqjdOdU4DB6SQrKwdLSxO50R5iRgV7lgWDy4SzrQlfZhZ/zJvCjmY/+R4rdrON3kiMLY1eGr1BrppZKgGPOGlIsCOEEMfYgAnGh5ivpm++HOuOKm5+/lEq6rdjjoQSk/8ZEiXjYcWAVYmj6DqWcBBXTzdtJgthxUyRy43Z5cLk85He1QaqhjZ1Gs/lT2GHKZvROc7kPDsuqwmnxUh1aw8vbG1hVJZT5tERJwUJdoQQ4hgaKMG4LNt5yKGjvvlyvvTiHylp2QPoaKoBXVUxaHEMWpy4QSWuGDBqcXRdxxLqxUWcYFTDp1rIyMtDnTMHFi8Gj4cGZxbvvFRDvt100ISCiqKQ77FS09pDQ3dQ5tURJ4UhXXd49913oyhKv9e4ceOS+0OhEEuXLiUzMxOn08miRYtoaWlJYYuFECezmlY/K97Yw5ZGL2l2E6OynKTZTWxp9LLijT3UtPoPOicQijDuzZdI7+kmZrKg6QooCpqqEjMY0VEwx2PEVAO6oqDqGmoshhqL4un1EY3GCOQXwVVXweTJUFpKIKYRisWxH2KlcpvZQDgWJxCJDbhfiOFmSAc7AOPHj6epqSn5ev3115P7br75Zv71r3/x9NNPs27dOhobG7n44otT2FohxMmqbziqMxBhdI4Tl9WEQVVwWU2MznHSGYjwwtYWNE3vd567tYnC5r10ZeWhWi2J4StdB11HRyFiMAI6Bl1DNxjQVBVFi+PobANVYeuE02m76hv9SskdZiNWo4HeQwQzwUgci9GA4xDBkBDDzZD/m240GsnLyztou9fr5fe//z1PPfUU5557LgArVqygoqKCN998kzPOOGOwmyqEOIk1dAepbesh32P9WENHeUqUXiXODnsamVk52P3dEIugxuNEVQVUlbimogOaDprBQCCngLopn2HLtLN4v3wqN00Y1+9+hWk2yrKdbGn04rQY+7VH13WavCEmFnooTLMdz49EiCFjyAc71dXVFBQUYLVamTFjBsuWLaOkpISNGzcSjUaZPXt28thx48ZRUlLC+vXrDxvshMNhwuFw8r3P5zuuzyCEGP4CkdiHQ0c20DTcrY2YggGiNge+nAJsZgMtvtBBQ0eqx01ObhrNwSi7s4oxd7ThCocwRqOYtAi6oqKgE1ON+ExW9haPZutlX6frjDOpbu9lYp77oKBFVRXmTsil0RukujURgNnMBoKROE3eEBkOM3PG50pysjhpDOlgZ/r06Tz++OOMHTuWpqYm7rnnHs4880y2bNlCc3MzZrOZtLS0fufk5ubS3Nx82OsuW7aMe+655zi2XAgxXB2q0qpv6Mheu4NJ76wlo35XchXyzuJRfHDq2VgySw4eOiopwX3KRCavf4uqgiLeCU2iWDNR0tWIIxLEoMWIqgZa3Fm8UX4qq069ACWnkuy2XjKdhw5aynNcXDWzNJks3eILYTEamFjoYc54mWdHnFyGdLAzf/785J8nTZrE9OnTGTFiBH/961+x2T559+udd97JLbfcknzv8/koLi7+VG0VQgx/h6u0GpXl5NTeZoqeeYKcSAB/9kerkOdUb2PC3r2kX34NhWmT+19UVeGii3DV1zO+oYFOm4X3xkyjpXcUxe0NxI0G1p5yHq+WTKLWkU1YA7c3yLTSdC49tfiwQUt5jotRZzuPugxeiOFqSAc7B0pLS2PMmDHU1NRw/vnnE4lE6O7u7te709LSMmCOz/4sFgsWi+U4t1YIMZz0VVp1BiKJSfqMFkwN9XTu2sHKag8XXTidOdXraQr62Zk7ApfFhFFVCVtsNGUVM6JlL5XVb6IyBzgg2KiogBtvJPCHP+FY9zalgSDYbLw38TO8c8pZNOSXoug6RdE4nb0R8j02Fk4pPKreGVVVpLxcnPROqGCnp6eH2tpaLr/8cqZNm4bJZOKll15i0aJFAOzYsYO6ujpmzJiR4pYKIYaTfpVWWXZK3t/AqPUv42pvRlMUunQj/pf/RlmwDcOk0QSDBroCEWLhGEZVJddtozhnNGn1u6CuDkpLD75JRQXhW7/D81kv09rUjup248vOR/9wZXJFUVBVBYvRQIbDjMtiGtwPQYgT2JAOdm677TYuvPBCRowYQWNjIz/4wQ8wGAx8+ctfxuPxcPXVV3PLLbeQkZGB2+3mhhtuYMaMGVKJJYQ4pvoqrSb6Gjjj789Q+tY6TKEQEbuDQHo2wcxcbFVbiPlaSC/I57TSLHyhGNG4hsmg4rYaUeJx2NkG/oPn2ulTmOGg4JQK3lEbiWs6mYqS7APSdR1/MIpBVZlUmCaVVEJ8DEM62Nm3bx9f/vKX6ejoIDs7m89+9rO8+eabZGdnA/Dzn/8cVVVZtGgR4XCYuXPn8sgjj6S41UKI4SYQiZG2t4bPrP0bhdveRdGhO68IQzyGo6sdU28Pe3OK0TsbYPNmlNxcPLYDel4CAbBawXXooSdVVZg3MY/tLX7er++mxRfGYzcBOt7eKJoOkwtczJ0glVRCfByKruv6kQ8b3nw+Hx6PB6/Xi9vtTnVzhBAppMXiNG/ZSbirG0t6GnkTxtDQHeSD6+9kdPV7pHe2ErXaiJvMiRN0HWt3J13uTEocKtaWJli4ENLTP7qorsO2bTB1KtxxRyIp+TBqWv089WYdb+7uxBuMAJBmMzF9VCZfmV4ilVRCfOhov7+HdM+OEEIMGk1j39P/xPf7P2Bo3EfEYKTdnc7eMeMonnsWZZ376LC6yNCa0Iz79dooCn6LnYyQD8ukKdDRBlVVMH48OByJHp19+yArKxEEHSHQgUQV1V2fq6S+q5fd7QEARmU5KEq3S4+OEJ+ABDtCiJOXpiUSht9/H99vfk/aa6+SHQ6hGwzErDZ86dl0dXfSWbWFAjVCpyePUL2CHomgWyxomk4krmE0mXBpURSjESZMgDFjoKUFGhoSQ1dTpyYCnf2WdDgSVVUYkelgRKbj+D2/ECcJCXaEECenqipYuRI2bEDf+C72lhZ0XSfidKEZTBgjYdJbGzBnRumMhNC1MBUVFfQ0ZWFqa8GnGFBVFYfZSKZRwxI1Q0cHnHkm3H57ojfH70/k6JSUHFWPjhDi+JBgRwhx8qmqguXLoa0N2trQAj3oug6KgikcJmI3ErHZMYWC2LxdWG1OQpE4mbtrSTtjCpH1b5Le2wtON2arCaWlJdGDU1KS6MExGgcuLxdCpIT8U0MIMTzFYvD66/DMM4mfsQ/XpNK0RI9OezsUFkJXF7qmoSkqcZMZRdMwhkOgKMTNZhRdw9HjJWhzELPbUdrbsEyagKUwH0vAj7J3b2Kl8tmz4dvf/lhDVUKIwSE9O0KI4efZZxM9NzU1EI2CyQTl5XDjjYmcmu3bobgYgkGIRFAUNRGw6DpxVUWNRVHjMTTVgEEHQzhMJNdJ6MqrcW//ALZvR8/KIuhwE8ovIDZ/AVmfn49qNKT6yYUQA5BgRwgxvDz7bKK82+uFnByw26G3N1H6fccdcN11EAolKqU0DcxmdFUlbjCgxGLEDUaMmk40GsdgBBQdPRYlOnosWZ+fDwsvYM+721j/3l5qggrNadlYoibKXt3N3AmywKYQQ5EMYwkhTiyaBnv2wObNiZ+a9tG+WCzRo+P1oo8aRcjmoFeDkM2BPmpUIgD661/BbE6UhHs89GZmE4xraIoBXVEwxqOJHh5dh95e9EgUf1YeGd+6BtVooKY9wG/rdV615qGXjmBkjps0u4ktjV5WvLGHmtZDz5AshEgN6dkRQpw4+iqotm9P9M5YrTBuHFx0USJX5s03oaaGYEYmnd4wwWgcTddRFQWbyUBmeibWffsS59TXo1dUUJNZQqazgQxveyKxOBpFBxyhADoK7TmFGL//PQrPOr3/Glk5ThQlMeeNy2rCaTFS3drDC1tbGJXllPlwhBhCJNgRQhx3mqbT0B0kEInhMBvJd1tp8oWS7wvTbB8FB31z3xxYtt1XQdXensi36Zuwb9MmqK9P5OO0tBANhWm2eIgSw2xQMagqcU0nEIkR0VWKQmFM48fD9u30vreZlrANX8UUqN1KRus+FKOBqMVG0Olm95jJvDL/qyxecAHw0RpZ+R5rMtDpoygK+R4rNa09NHQHZaVxIYYQCXaEEMdVTauf1VtaqG3rIRSLE4lphKMaFpOK2ahiNRooy3Ym8l069g3cc/OFL8A//pEIdCorE8nEAG534v22bbBqFdqMz9CrG1CDQWz7TR1vUBVsqgHN10OvbsA1ZSr102ZS/Zv/I7ZlGzEtSlVmMcHyKcTLy9GKS+gqHElnTj71nYkgDRJrZIVicezmgRfhtJkNtHwYxAkhhg4JdoQQx01Nq58Vb+yhMxAh32MlFDWwcW8n3kCYsZFOJqabwOViazhKdOtWrtz4T9w9Xnpy8olk5mEOB3G++y7q1q3Q0wNlZR8FOn0UBYqKoKqK5vM/hy+7kPyGXfhcTuK6khzGMig6af5uGovK6Mgu5/nt7TTMuoxIyV6y9DAhq51d1gwMJiOjc51kO60Q1bAYDTjMif9VOsxGrEYDvZEYLqvpoOcNRuL9jhdCDA3yX6QQJ5EDh5P6DR8dh3ut/qAJ9uxhhlXD3NLDJm+cSS1tTGnaQVbjHtzEcaW5mFpUSri5hUZ/BztHjaGrNUpMC2NUVdLt+YzfuxVHZxtMnDjwzRwOaGgg7O/h5fO/xKK//gr7vr102tMJmc1YIxFcvV0EnW5emX0prTs76QxEmFiczjuawjZ/CJvJQKg3Qnd3kLaeMNlOCzpwZnkWhWmJnpzCNBtl2U62NHpxWoz9hrJ0XafJG2JioSd5vBBiaJBgR4iTxIHDSf2Gj45DuXTLhk2U/m4F5+3eQmZrA4ZgLzPjYI7HCNvs1BSNZZcnj5E2KNz2Lo76vbxbMJaQL0SG3YzJYCQa12jtCaMYPUz27cLc1JTI1zlQIABWK5b0NN6dNJMmb4jPv/o3ijsbSe+NETMYqc0p5V9nLmJXxRk4vUEK022oqkp5jpP2njB7O3tRFLAYEzk+PeEYqqLQ4g+zq72H8hwXqqowd0Iujd4g1a2J3B2b2UAwEqfJGyLDYWbO+FxJThZiiJFgR4iTwIHDSXazjd5IjC2NXhq9Qa6aWXpsA56qKqyPPczIrdvI6OlEjccJ2lw42xoxxeNoqoERzbvxGy30pufjzy7AU11FVlcrvrJRmD+cnM9sNJBpVGmLpeNTLWTU1aEUFuILx4nGNUwGFbfFgLJvH0ydSk7laMLvbOSFUaeyc/IMxu6twu3vwudKZ8eICvb4oxRGYrgsBuwfDjWl2004LAaMBgV00HSIazpZTgsTC910BKL9KqzKc1xcNbM0GTi2+EJYjAYmFnqYM17m2RFiKJJgR4hhbtDLpT9cjsHS1YlRi6HEYvSmZ6KEQoCCpqoouoYpFKSkrR5vcT5B1YTfbCe7p4t4sAfdkr7fBRUyiNGUmUfc5sa/9i0anFn0mizYo2EKe9rJGlVE2sKFNPVEsJhU0u0mOiI6H4ycgMmgEo1r9IRipNlM2MxGdF1J5t34QzFCUY2S9ET1VDAaJxbXmVKShsdmxmw0HFRhVZ7jYtTZzkEbEhRCfDoyqaAQw5im6byzt5N367pwWg5eyuDAcun9Tjz0xH1HUlcH27djy0onI+THb0kECEY0VCBsNGONhAkbTWT0enGHAwRsDtodaTijQWzaAZVMuk5aVwtVJeP5zWe+xJa8MtJCPkZ2NZIW8rElr5zHp11ITWYRgUgMs1Flakk6OS4roahGd2+EUFQjx21l2oh0PFYT+R4bTd5QYpXzuEYsrmEyJqrD4ppOrseK+8MEZJvZQDgWP6jCSlUVijPsjMtzU5xhl0BHiCFMenaESKHjmTDcl6Pzbl0nWxt9eGwm9nWFKM9xkuEw9zWA3M5mDE3tRGoNkDYeduw4/MR9R+L3QyiEkpaGywh+g5lgNI6Cmlg7SgNN09AVFasSRwuF8Wlmoul5lAS7cbU1EbNYiVrtmEK9uNqb8TrTeGnsDEI5I3B+7Xo62powBQNEbQ682flUt/di3trC5yblYzUasJoMnFqajj8UIxLXMBtUXFYjPeEYVpPG7Mocnt/STHVrD06LAVVVCIRjRGIaNrOBsmxHsgdMKqyEOPHJf71CpMjxTBjuy9Hp9vYyrW4bJbv24XensTl/LI2N9eSmG8gL+cjb/j6uvbXovUHyNmVDfg40N0M8fuiJ+44U8LhciQApHsdssZCpKnTGFAK6EavJgrW3h7jBiEWFKCoBjBR6bDjbdD6YPBNLXg6ZDXtwdrQQN1toKa/k36NOZ5+rgNOznCgGA768ouTtFEj2TumQrJYanePEbfuoPHz/aqnPlGWR57GyeksLNa1+FKC7N8qITPuHwaDloHOkwkqIE5cEO0KkwPFMGO7L0Sl4/SW+/srTeBr3Eg+FE4m3ZgvNniwMFivF3mbiRhNVBaPRS0YRSzeivfgiam8vzJuXmLAPDpq4j7FjEzMaH0pJCYwbh3/9BrpVG6b2ViLONEAh7EnHHQ5gtBhxGGJECgqZMiIdZ3sTvjElvDDtQnZ6Chgb6cIdC+EzWtlhTgeDSmYohsMy8P+y+ibzC0bjR10ttX/eTVWzj3+/30Q4lkh6jmmaVFgJMYxIsCPEcTbQUgmrt7TQ0RMhz20hHNPQ9Rguq5HROc6DEoZjoQg7/7mGYEMT1vwcPKNGEA30YklPI2/CmMTQ0H4auoOYVz/H5/6yHHPAT4cjnZjdRm5XC56AF0fAR7snk4gWJxTVyamrZZ/Fznt+C+N7Y7h0BfOOHficaUQ1PVHxZDWifDhxH3V1UFp66AdWVfaeNYfmde/hjCtkGo1kBLxETWYIBel2puOxqFhMRkwuB/T6YNo00hYu5HOZRR/2dpkIxxLDRxNynEwq8vD3dxuOajK/4gz7UVdL9eXdFGfYGZXlkAorIYYpCXaEOI4GGqrKclrY3NBNJKaxpyNATNMwqioZRpjcuJ3xvk46HOnsrcjCu/JfqL/6NZnNdeREQhhjMSImE76cItoLS9g7eiwFV32ZEZ89NXnPQG+I6c8+idHvZ19GPgaDSnZXC6qq0mn34An1kNvRxO7sEWgWK7kRP9aufbTnlRAJR2i02rDt2scOcx49NkdiYj+HmfIMCxmhUCIn5zA0TefZSBrt517KudvfwLLjAzxN9diCPUQtNhoy8tk19VROv3Qean5ev/WvymHAKieA9+u9Rz2Z3yeplpIKKyGGLwl2hDhO+oaquvwhxgTbSW/YSzAa5y1TJpt1Nxk2ExWRToo7Gsjf8QGTqt4m19+BSYsRNRgJ/fGn5Aa8qJpGr82BORJCQcMe7iWvaS973Gmom9+n+b56+N53kgFP2vsb0Zrr6XSkYTQZMEcjWKJh4iYzRoNKJGbCGerFqcQwOi1oEbD7urHmFKKYjPRGNJRoGDsxTHZzYmI/f4hIZxeTbAbcrsP3cvQtlplWWcE7p0zA3dqIKdCDpbeHsN1Bl9FGnSOLwlPHDbhYZl9vy4E+7mR+h7rO4XySc4QQQ58EO0J8GgOs0K1pOk2bd/DCqztw1+1j/vY3Kfzgbew9PnR0ZlmcbMsagdmoMr6jjrTOVpyhHtDBZ3HQ4skGXaOseQ+qrrEvuwhrJIxB0+i1OkHXcYZ6yKmroW7O57HU1tD0xJ8pPmMKqtGA2taKIR4lZLZgBFRNQ9E0NGMizyZmMAI69liUCBA3mjAHA8RNJtqtbtLam4mYzMSNZhRFSUzsZ1Aw79zFtsmncHpR8WHnrOi3WKaq9EsmBohpGqH2wMdeLFMm8xNCfFIS7Awhg7lu0YlkyHwuBwY2gUBiJe79SrS7rE72dvQSbGljamsrJW112EO99FrsdKdloOsK7u525u74LwA9dhfGWAR0iCsKzmgQxddGt/2jFbuzutuJGk1EjaZE6ZGiEDJZcAV8GJqaiOYVYNixneYtOyk4pYJgeiZWkxl7LEKvwUhMUdBVFUWLE1cMmNCJqwaM8USwY4hF0QxGgqqR1swiTmtvJIpOXNcxxOPJ8m9fZiZrKz5DoS982N6P47lYpgw1CSE+CQl2hojBXrfoRDFkPpeqqv5zz4TD0NSElpZGT/lYIpl5xPbsxbT6FQp1jd1jp2CKR7CFghjicYzxKIoGEbMZHTBpMXQUlFgUczxGxGBEUw2Y4jFs0RAEFRQgqhqxxCIAREzmZHNiBiPWaBhDqJdIfgGmlibCXd0AqDM+Q1d+CXn7amm02QljJmi0YAsH0c0qtliEbqeHqNODvbsDNR7Hn5VHTAePv4udJRV0uDIoC/iw+juImy20lo9nx4xzqbfnHbFH5ngvlilDTUKIj0uCnSHgWJQhD1Tx0+QLHfN//R6pl+Vw+z/uvprWHn79SjWN3UEyHBZy3RaMqsqWRi9NXQG+XqRTuv196O2F8ePhM58Bo3HAoaXDlkofSVUVLF8O7e2JuWfsdnjlFaL1DXR19bJTSafb7qZoazVpqNjNRvLaGtB9XeiKQq/Fhikew+HvQnen44iG0BUVXQd7NIyqaWgfVlTFVQMGPY45Fk3cW1FQNB1IDEdphsRxxngMTVGJW+2ogQCaxYIlPQ2AwiwXz33pKtyPPEBRVxM97gziaR5M7UHsAS9hs4VdoyejWCyU79uJomnEzSZcAR8bi8eydtwM4mPGco4tiDnUS9TmwJdTgD8Sx9IbPWKPjCyWKYQYaiTYSbFjsW7Rgb0fkZhGKBJHV0BVwG42MrHQw7wJeZ+oN6QvEKlq8vHOni7a/CHCce2gXpbD9cIA/GfTPnpffR1TVzvR9CzsZ32WeVMS+RyrP2iis6oGJeBHd7jQiot4a1cn8T27GdFWR2avj253OuGy0UxIN3HaX39P1va30UMBFF3/aJbfyy+Hrq5PPvvvwQ+f6NFpb0evqMAXjhNv6cDc0U2HKxNToIeC5r0Yistw+r0ELHZCqkqmrxM9Fk5cwmAgoihYImEi0QiqrqGjgKKjoKMrYAA0hcR2HRRVIWI0YYlG0ICw2YIpFiWsGkDXsUbDeJ1pxPPzsdTWEJ18CnkTxgCJYGPcNV9mTW+EU//5R/Lb9mGMx4iZrfjtLnqy8ijLtNMQ0nnjtDn4Jk0hnp2D12DheZ+Z3pjOrBwnfmdW8mP4uD0ykl8jhBhKJNhJsb7KlXyPtV93Pxy8btFAXfc1rX7+3+u7aegOkm43Y1RVtrV4aQ9EUBXw2EyYjQZ2twXY3uznptmjP9YXTU2rn9UfNFH3XhWt+1qwBHooNGkUZjrwF49kaziTRm+Qc8fl8PL21sSMvc07yAh00+lIY2NwLFXNPka++QqzVv+ZgvZ9GGMxYkYjjX8r4h9zL6O3uJSJb7/MZ9vrscYi+DCyM2pmvL+bU5qrye7pwqTFiKkGuq1uTIpOetALKIQcDlBVjOEQhvfeQ926FSZMgOnTP9nsvwf6cJ2nrswcqvd20xWIYO1qp7Q7gNfuJs3hxOXvxuvrxqjFiZjNRDSdWEzDZDJCmERysKKi6lF0XUdX1ESQA8QMJnQ1UTEVwYSiJH7vmsFIt8NBfmfz/9/encfYUZ19Hv9W1a2qu/dy27cXt9u0d8AbxnQDTsZ5g4MnsZh4ooTwDoksmIlmMYqNJRRIBChKwAEmyMJBGCIlIzEhAaGXLGQb9kUsNiY29ot3vDTd7n25+1JVZ/64dkODk5DQ7muK5yP1H7euu/vp07brp1PnPAd0nWwoSiSXJlzIYHgupYBNf9sc7COHceoSNK+7ZkK/nTnJGGxYx59XrsJ95VWCo4MUahsIXNbJlxIejbYiX9R4ddTiyFBuvKfNZ5pM+tJFhrJlrIDxsWZkZH2NEOJcIWGnijxPcWQgQ3+mQNQOoJT6UOA53Rn2Q+skPA/v2HGefnIX7/bn0V1FcLCbVKGMEWsiUD+NJT0HaSmloSHJG03z2N01yi9eOcZ/nWlQHh0bb0oH0Lv3IMWR0cq1C+ag93Rz4lgvLz7/FtP37uKSg2/R3HOUmlwKPEXJClJKNNCztJMnO6/i/wzl6Hz7Ff7b849Td/IERrmMa5r8S3Mbz9fN5rNvvUC8lCMVq6MUDGIVCrT1HuOrD/+Yk8lW6pJ1ZKa1MBIMUjh6jM//+0vECmlAwzUC5KwQZrlEMjVAQHkoTWMkXIPr6uACepC6cgGrVEI7eZKUYVPOO5hmiPj556Pt2/fRuv9+UDpNejTNX3JBcl6ZmB3ACgcpawaGUyalWdjlMrqm4RkGuutgK8gHLMrxGPFcFsspV9bkaDqFgE0pGCZcqhy6mQ9GKIZCJAdOYrllFICuU9IN7FKRwXg92UgtoXwGDQ2FTs4OMpicjhuL485fQPO6ayb02TltTjLGrFXz6V7edsawcR7wP8/w+PCdwcykzcjI+hohxLlAws7Z8jfWjXiOyxsv7eKN3UcZOjmEltM4HI+jTW9lWSDLNErj6yRy+RI1PScYeOxtiiGTxLKFtFig/+63DGzfxUVvH2X1aB/xQg40KKDjaDqG55765SqwLHqntfLneZcSfTpDV64Xyynh2UFO1NWhFARGR9CLBSy3TBmHSE2M4nCaL/Z0YepQLJSI5TMoVOVRi+OgjYzQ/uqzrO3r5enkAr6680nC+Qy52gSOHSJQzFN//BBX791J0TDpbpmFblTGoBiO0GcFmdl9iEh3nr1Lrsa2LYplh/hAL1a5SMB18XSDlBVC0zU83SBULqCjcBXYTpG8aaJrGrrrooCS0lC9/ezb/jZDicbxhnjz6pPUfpTuvx/8NUaidBfAK2dINNQDGrlQlFSkhmnZYdJAQWk4tXVk43XERgYwNBiIJSidNxc7lyHc34vtlMiGo0QtHatQCXCaplEbNiFZT8kAve8khlPGQcfVdPpaZ+PdsJ6F1339Qx2UQ9kctX+lg/L7/b2wcab3ZUZGCOE3EnbOhn378P7tCfJv7cXN5zFCIUKLF6J/5T9zfCjL4Qcfxt65gyuHTxIuFcibQUaiNSgjgGMHicUj6OEQI3aMdE8f5518h5p8pWttyQ7SH7KIzmzjOGESo/1MSw1jKJdCwMYL2DSnB9GUImsG6alvxjR0Zr57iP9+bB+HEzMYWbiUaF0NRk8XM156GoDuhRdjJBqo37sTa2yUkVCUYsAm6LgEi1nqizmKukk+FAUgWCpQUJBWOg3HD3H1/rcI4TI2vQ1XaXhK4QQjOJEyTSODeJoOSk0YJtN18LQAVrlIsL8XNaMNM5OmPjWEoRRK00ApDOXhYaChQKusaQGwXIfyqUW7eiWCodBQjkPUKeC9ryFeJguXlDPE/k733w/qjk/jSH0r7V0HGEvUgwaGofNu00xiJ7IkU4P01jWRsULEmqdjD/bgeTBQMw07VkvvnAtIFoqEc2lMwBgbJh2t4eSyS2mJB6k5vB+GBwnp4J0/n+Hp59G3eDnasmVc8J++QCBY2YF1wdVr/vm/j/8EmZERQviJhJ3Jtm8fo3f9bwbf6ebdaAM5q55wukjrn18k+vLrjKYKxAeHqUsNYeORC8cIZtPM7hnEMwKMxOo4UreY2qLD7O1/IlLIkgnFGKtJoKFoHOjGGinRmysRtELUZUcpaTrFYIRQKU9DdgSlwNEDWJ5LPJ9mtKGZfMaiLp8lmRlhIBwBQyfc13uqd4tGqK+X8IiOWyrTXd9MIjVEbWaUVG0D5NLonoehKzgVOEoBk6BTYkiPEcxlqMmMMJScTrro4Xge6lQuiZfKeGiYbplwKUch8N5jEEN5KF1DcxRWIU8RsNwyputUgs3p+KIUSlWCjIcOuGinrnueh6PpoDj1GQpH08mawfca4gV0sgPDdHuKeZHo32yI90FZx2PnspVMTw+SOHGYdEMTWjBENmgzGoyjdJ1UJE59z3GMcIgjl11BX6pAbS5F7MQ7lGyb41ddzfQvfJagAQXHxZi/gPmLF1RmSo4dg4MHAdDnzaPhvPNo+Dg7x4QQQnyIb8LO/fffzz333ENvby9Llixh69atdHR0TG0Rnsfgw7/i5MEujjfOJBY0qTV0yq7NfjPIwu3PUotiOFKLpTxSsTpAI5ZPY3kuY3aYgOdS/+5xDE1hOiV0pdADOq5lYzkllK5TMkxqUyPU6KPoQNGs9G7x0LBch2LAxNV0DM8jUspTKmQrj1GsMDWFNE1jAxTLMcKpEQrhGBoQH+lH1zXSdgTTNCjbQWoyo2iOg648PCpfz/A8XMPA03VMt4xu6Ghu5c9klE7J9QjoGqcncsp6AA8N3VOYjkvhfcNVaXR3agYnUplFMII2yjTfm6eprNgFwNF0SoaO6Z2OQUx4TylFQHn0heIM1k6jfvwbQUt6kMNtC4jEpzHjH/iVRqwAozPn8Mqaf2XxG89T3/UO0aE+bN3krfnLeHZuJ+VQmMuTFm4kygGrjrqwydqESz2lv3pY57hZsyofQgghzhpfhJ1HH32UTZs2sW3bNjo7O9myZQurV6/mwIEDJJPJKavDO3acwTfeoq+mgUTUpnJLBitg0OAVUI5DQLnUp4bJR6KgaZinzi0q2iFCbgk3VEtTbhjDddAVFINh7FIR0ymheS4oRSFgESoXMMsu5YCJGp8JqMy8eJV5DwAMFLpTRvM8igGTUKlMuFykVLbQXRfPNCuPilwHzQUVrXS8dU2rsjPIdfB0g8pOaa+ym0hVer4oTUd5Hq5uoE41xCuMz8hU5IJhygGTULlIEX18xkcpyFHpKVO2bE5GEkQdFy8cI5dIEh4bqczcaDpK1zF0Dc8DTzNwNIOA8jCUh+45BJSHXa5s886bNkOxeqLlApprjXf/zdYlePOi/8Acx/uHfqenG+TtKU+ncPW3qBk4iZnPUg5FOBZOcPLEKKau8XYiQtCsnNAtW6uFEOLc4ouwc++99/Ktb32L6667DoBt27bx+9//np/97GfcfPPNU1ZHf88AhVQGqy3J+2/4AFq5VAkMnkfALZ86nwh0z600dTNtzHIRpWnYnotRLqMBTiCAUSqiey6upuNp+qlZjfce5wRQlSMBKmcJoJ9eRqxVZntKegBP0wi6DpphUA6GUaZdWety+vvoATSt0qzO0S08TaNk2pieR9YKEizl0U8lFaUUllOmYIcIeg5OOMyobZIo5yjqtThKobxKqDENHSyLIoqa7Cgjhk7RsrFLRRozo+Rr69HnzWP+aDfdTgMp08ZsaKKxrws8BwUES3nKukHIddA0SIVjFAyTiFMiXCqgKUUxYPHvTbP5zQX/QqtW4LPFIQLd73X/fWv5SkYTbf/wEQUTGuQN5miubSSUrGzHHhwrsHxmHV9a1ExDzJaFvEIIcY76xIedUqnEzp07ueWWW8av6brOqlWrePXVV6e0lqwdohCwCDtFyrY14T1l2pX+KegQCKCVyyjbxtONysyF6+BpGp7rYdgWrgKjXMRwHJSu4+kGJcMkb9pE81k8DQqWjaEUZqmysyqgQdkIEPDcysYvTaMUikAshlfIEMuMkEskSU9rAg1y8Tqiw/2gaYzVN+C5ikRmhLRhYuezDE9rIaR5MDyCqxvguYSKOdANMAOEAjplz6Fv7iL2zF7Clc89Pt6xt2gFsUsFoqlhColpvLR4JYu79lHXcxwjP4YbMMnNW0Bgw7eZfvFC6v/tCZrf2oubH8ZoihG66BoYGsZ57XXMvl4iTgllmgxE69m3+DIemPM50hh09uwn4pY4lJjBS8l5OLrBZ9rrMYP58RmYsWnNHBrMsSgZ/aeOKJAGeUII8cn2iQ87g4ODuK5LY2PjhOuNjY3s37//jJ9TLBYpFovjr1Op1KTUYrW3M9Q6q7Jzp33e+HoSABWPoRkGRQVuIkl0eIARw0QZJkXTJpoZIxWOE1IOoZkzGM4UsA4fwC7kyMRrKQcsNGA0FCeWz2B6Hv0NTUSVS3SoHys7RsEMMhytI5kZJuC5eNEosZYkNZqHbniULZvBaAItncaLRMg1NlHX340Cio0tjKoAscNjJAe6yUTijMw9n5JXJlHeyxgKTXnUnNr6XQ6YpCNxTiy6hOD/+h+8kYqgtc3g0t8/Ql3PCaLpEbyAydDMuby25l/ZceEKln+uHbVzB/mTvZjNTcxYtRLdqjw202+ZT+SDW/UB69ixSjfkgQH6g3F+1mfizZxJS67MrhOj/LqhFddTGLpGjXnqcZ6h0/2+GZiTg7mPfUSBbMcWQohPrk982PlnbN68me9///uT/nWn10d4afUaBv9vD03HD5Oe1kQ5GK6sGxnopad1NmXHI1HOYlgm9bkxcoZJyass5I2qMmYsTHDh+bjDYzgnjqGcEsrxCJQqS3vtQpacFSIXiVFsbkVXDoauYaVToCBsGehtM9BdF93zCIwOg2nCsosY/vx/ZPDguwQOHcDsO4ln23R99guVhb2jI9QU0vTWNTESTxCMhYnnMxQDJq91rubEnIVYjUnKI6NouQxmIEB44flcdsXFzErGef35I7w471JOXvo5pu/fTWhsiHxNgu4FSzg0XGBRMkrrtDj6l1adefB0/cz9b963gLfBU9Q9f4S9PWPMTUaZWR/m5FiBXNklFDDIFB2m14WoD1u8M5id9BkY2Y4thBCfTJ/4sNPQ0IBhGPT19U243tfXR1NT0xk/55ZbbmHTpk3jr1OpFDNm/CN7dM5M1zU61qzgyUyR8176f7QPdhFx+igGTN5unsOxz36BzvZ6Uk/8Gm/3G9T3dVNXyKHiUZg/m0g8gh4KwvAw8WCQka99lcOHuoge3Ec8NQxAOhxn55zL2fH5r9A8PUHcKZDSLQZTeWalernygiZqO5ZAayts3w59fdDYCJdeSmMgwDTHndgt+QMdlAeweL0cZuTAUfRsGi8SI3HBHL60qJlZDX99ZmN8XctwgczcJe8dMzA8eQc/numAycaa4PhxBg0xm//S2fY36xRCCPHpoyn1gU5vn0CdnZ10dHSwdetWADzPo62tjRtuuOEjLVBOpVLU1NQwNjZGPB7/2PWcPk9qeN/hCYHhykXNzEnG8E4HjqFhwsU805ob0OtqKwHl3XcnPMrxPMXJ3fsYfHMvAIllC8m1tPLUvkGODGTGzzSaM4m7gP7eyeZ/8+c+ta7lbNQ11d9HCCHEue2j3r99EXYeffRR1q1bx4MPPkhHRwdbtmzhscceY//+/R9ay3Mmkx124J8PDOfK1z/X6zpXf34hhBBT56Pevz/xj7EAvv71rzMwMMBtt91Gb28vS5cu5U9/+tNHCjpny9le33Gurh+ZqrrO1Z9fCCHEuccXMzsf19mY2RFCCCHE2fVR799yCI8QQgghfE3CjhBCCCF8TcKOEEIIIXxNwo4QQgghfE3CjhBCCCF8TcKOEEIIIXxNwo4QQgghfE3CjhBCCCF8zRcdlD+u030VU6lUlSsRQgghxEd1+r799/ojS9gB0uk0wKScfC6EEEKIqZVOp6mpqfmr78txEVROSe/p6SEWi6FpH/8wyVQqxYwZM+jq6pLjJ6aAjPfUkbGeWjLeU0vGe2pNxngrpUin07S0tKDrf31ljszsALqu09raOulfNx6Pyz+YKSTjPXVkrKeWjPfUkvGeWh93vP/WjM5pskBZCCGEEL4mYUcIIYQQviZh5yywbZvbb78d27arXcqngoz31JGxnloy3lNLxntqTeV4ywJlIYQQQviazOwIIYQQwtck7AghhBDC1yTsCCGEEMLXJOwIIYQQwtck7Eyy+++/n/POO49gMEhnZyfbt2+vdkm+tHnzZi655BJisRjJZJK1a9dy4MCBapf1qfGjH/0ITdPYuHFjtUvxre7ubr7xjW+QSCQIhUIsWrSIN954o9pl+ZLrutx66620t7cTCoWYPXs2P/jBD/7ueUvio3nxxRe56qqraGlpQdM0fv3rX094XynFbbfdRnNzM6FQiFWrVnHo0KFJrUHCziR69NFH2bRpE7fffjtvvvkmS5YsYfXq1fT391e7NN954YUXWL9+Pa+99hpPPfUU5XKZK6+8kmw2W+3SfG/Hjh08+OCDLF68uNql+NbIyAgrVqzANE3++Mc/8vbbb/PjH/+Yurq6apfmS3fddRcPPPAAP/nJT9i3bx933XUXd999N1u3bq12ab6QzWZZsmQJ999//xnfv/vuu7nvvvvYtm0br7/+OpFIhNWrV1MoFCavCCUmTUdHh1q/fv34a9d1VUtLi9q8eXMVq/p06O/vV4B64YUXql2Kr6XTaTV37lz11FNPqZUrV6oNGzZUuyRf+s53vqM+85nPVLuMT401a9ao66+/fsK1r3zlK+raa6+tUkX+Bagnnnhi/LXneaqpqUndc88949dGR0eVbdvql7/85aR9X5nZmSSlUomdO3eyatWq8Wu6rrNq1SpeffXVKlb26TA2NgZAfX19lSvxt/Xr17NmzZoJf8/F5Pvtb3/L8uXL+drXvkYymeSiiy7ipz/9abXL8q3LL7+cZ555hoMHDwKwe/duXn75Zb74xS9WuTL/O3r0KL29vRP+T6mpqaGzs3NS751yEOgkGRwcxHVdGhsbJ1xvbGxk//79Varq08HzPDZu3MiKFStYuHBhtcvxrV/96le8+eab7Nixo9ql+N4777zDAw88wKZNm/jud7/Ljh07+Pa3v41lWaxbt67a5fnOzTffTCqVYsGCBRiGgeu63HHHHVx77bXVLs33ent7Ac547zz93mSQsCM+8davX8/evXt5+eWXq12Kb3V1dbFhwwaeeuopgsFgtcvxPc/zWL58OXfeeScAF110EXv37mXbtm0Sds6Cxx57jF/84hc88sgjXHjhhezatYuNGzfS0tIi4+0T8hhrkjQ0NGAYBn19fROu9/X10dTUVKWq/O+GG27gySef5LnnnqO1tbXa5fjWzp076e/vZ9myZQQCAQKBAC+88AL33XcfgUAA13WrXaKvNDc3c8EFF0y4dv7553PixIkqVeRvN910EzfffDPXXHMNixYt4pvf/CY33ngjmzdvrnZpvnf6/ni2750SdiaJZVlcfPHFPPPMM+PXPM/jmWee4bLLLqtiZf6klOKGG27giSee4Nlnn6W9vb3aJfnaFVdcwZ49e9i1a9f4x/Lly7n22mvZtWsXhmFUu0RfWbFixYdaKRw8eJCZM2dWqSJ/y+Vy6PrE26FhGHieV6WKPj3a29tpamqacO9MpVK8/vrrk3rvlMdYk2jTpk2sW7eO5cuX09HRwZYtW8hms1x33XXVLs131q9fzyOPPMJvfvMbYrHY+LPdmpoaQqFQlavzn1gs9qH1UJFIhEQiIeukzoIbb7yRyy+/nDvvvJOrr76a7du389BDD/HQQw9VuzRfuuqqq7jjjjtoa2vjwgsv5C9/+Qv33nsv119/fbVL84VMJsPhw4fHXx89epRdu3ZRX19PW1sbGzdu5Ic//CFz586lvb2dW2+9lZaWFtauXTt5RUzavi6hlFJq69atqq2tTVmWpTo6OtRrr71W7ZJ8CTjjx89//vNql/apIVvPz67f/e53auHChcq2bbVgwQL10EMPVbsk30qlUmrDhg2qra1NBYNBNWvWLPW9731PFYvFapfmC88999wZ/79et26dUqqy/fzWW29VjY2NyrZtdcUVV6gDBw5Mag2aUtIiUgghhBD+JWt2hBBCCOFrEnaEEEII4WsSdoQQQgjhaxJ2hBBCCOFrEnaEEEII4WsSdoQQQgjhaxJ2hBBCCOFrEnaEEEII4WsSdoQQQgjhaxJ2hBBCCOFrEnaEEL4zMDBAU1MTd9555/i1V155BcuyJpyuLIT4dJCzsYQQvvSHP/yBtWvX8sorrzB//nyWLl3Kl7/8Ze69995qlyaEmGISdoQQvrV+/Xqefvppli9fzp49e9ixYwe2bVe7LCHEFJOwI4TwrXw+z8KFC+nq6mLnzp0sWrSo2iUJIapA1uwIIXzryJEj9PT04Hkex44dq3Y5QogqkZkdIYQvlUolOjo6WLp0KfPnz2fLli3s2bOHZDJZ7dKEEFNMwo4QwpduuukmHn/8cXbv3k00GmXlypXU1NTw5JNPVrs0IcQUk8dYQgjfef7559myZQsPP/ww8XgcXdd5+OGHeemll3jggQeqXZ4QYorJzI4QQgghfE1mdoQQQgjhaxJ2hBBCCOFrEnaEEEII4WsSdoQQQgjhaxJ2hBBCCOFrEnaEEEII4WsSdoQQQgjhaxJ2hBBCCOFrEnaEEEII4WsSdoQQQgjhaxJ2hBBCCOFrEnaEEEII4Wv/HyissFuIydnfAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.linear_model import PoissonRegressor\n", + "from sklearn.metrics import mean_squared_error\n", + "\n", + "np.random.seed(42)\n", + "n = 100\n", + "x = np.random.rand(n) * 10 # predictor\n", + "beta_0 = 1\n", + "beta_1 = 0.5\n", + "log_lambda = beta_0 + beta_1 * x\n", + "lambda_ = np.exp(log_lambda)\n", + "y = np.random.poisson(lambda_)\n", + "\n", + "data = pd.DataFrame({'x': x, 'y': y})\n", + "\n", + "plt.scatter(x, y, alpha=0.5)\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.title('Generated Poisson Data')\n", + "plt.show()\n", + "\n", + "model = PoissonRegressor()\n", + "model.fit(x.reshape(-1, 1), y)\n", + "\n", + "y_pred = model.predict(x.reshape(-1, 1))\n", + "\n", + "mse = mean_squared_error(y, y_pred)\n", + "print(f'Mean Squared Error: {mse}')\n", + "\n", + "plt.scatter(x, y, alpha=0.5, label='Observed')\n", + "plt.scatter(x, y_pred, color='red', alpha=0.5, label='Predicted')\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.title('Poisson Regression Fit')\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bcb97615-c87c-4cff-bc67-353d8b55dcae", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Assignment1.ipynb b/Assignment1.ipynb new file mode 100644 index 0000000..0f402ee --- /dev/null +++ b/Assignment1.ipynb @@ -0,0 +1,394 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "68c4bfd2-cb36-436e-b12b-f718b597db6b", + "metadata": {}, + "source": [ + "**Question 1a:**
\n", + "$n \\to \\infty$
\n", + "$p \\to 0$
\n", + "$P(X=x) = \\binom{n}{x}p^x(1-p)^x$

\n", + "$P(X=x)=\\frac{((n) (x) ... (n-x+1))}{x!}\\frac{\\lambda^x}{n^x}(1-p)^{n-x}$
\n", + "$\\lim_{n\\to\\infty}\\frac{1(1-\\frac{1}{n})(1-\\frac{2}{n})...(1-\\frac{x-1}{n})}{x!}\\lambda^x(1-\\frac{\\lambda}{n})^{n-x}$

\n", + "as $n\\to\\infty$ the pdf will reduce to $\\lim_{n\\to\\infty}\\frac{\\lambda^x}{x!}\\frac{(1-\\frac{\\lambda}{n})^n}{(1-\\frac{\\lambda}{n})^x}$
\n", + "given wkt $\\lim_{n\\to\\infty}(1+\\frac{1}{n})^n=e$ then $\\lim_{n\\to\\infty}(1-\\frac{\\lambda}{n})^n=e^{-\\lambda}$\n", + "

\n", + "using this we get the pdf of poisson distribution as $P(X=x)=\\frac{\\lambda^xe^{-\\lambda}}{x!}$" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "f6419954-c9c4-4189-94b7-11b7507e967e", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "<>:22: SyntaxWarning: invalid escape sequence '\\l'\n", + "<>:23: SyntaxWarning: invalid escape sequence '\\l'\n", + "<>:24: SyntaxWarning: invalid escape sequence '\\l'\n", + "<>:22: SyntaxWarning: invalid escape sequence '\\l'\n", + "<>:23: SyntaxWarning: invalid escape sequence '\\l'\n", + "<>:24: SyntaxWarning: invalid escape sequence '\\l'\n", + "C:\\Users\\Sathv\\AppData\\Local\\Temp\\ipykernel_16276\\1208199782.py:22: SyntaxWarning: invalid escape sequence '\\l'\n", + " plt.plot(x, pmf1, label='Poisson Distribution with $\\lambda$=6', alpha=0.5)\n", + "C:\\Users\\Sathv\\AppData\\Local\\Temp\\ipykernel_16276\\1208199782.py:23: SyntaxWarning: invalid escape sequence '\\l'\n", + " plt.plot(x, pmf2, label='Poisson Distribution with $\\lambda$=4', alpha=0.5)\n", + "C:\\Users\\Sathv\\AppData\\Local\\Temp\\ipykernel_16276\\1208199782.py:24: SyntaxWarning: invalid escape sequence '\\l'\n", + " plt.plot(x, pmf3, label='Poisson Distribution with $\\lambda$=2', alpha=0.5)\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np \n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "\n", + "mu1 = 6 \n", + "mu2 = 4 \n", + "mu3 = 2 \n", + "\n", + "def poisson_pmf(k, mu): \n", + " return np.exp(-mu) * (mu ** k) / math.factorial(k) \n", + "def binomial_pmf(k,n,p):\n", + " return (p**k)*(math.factorial(n)/(math.factorial(n-k)*math.factorial(k)))*((1-p)**(n-k))\n", + "\n", + "\n", + "x = np.arange(0, 10) \n", + "pmf1 = np.array([poisson_pmf(k, mu1) for k in x]) \n", + "\n", + "pmf2 = np.array([poisson_pmf(k, mu2) for k in x]) \n", + "\n", + "pmf3 = np.array([poisson_pmf(k, mu3) for k in x]) \n", + "\n", + "plt.plot(x, pmf1, label='Poisson Distribution with $\\lambda$=6', alpha=0.5) \n", + "plt.plot(x, pmf2, label='Poisson Distribution with $\\lambda$=4', alpha=0.5) \n", + "plt.plot(x, pmf3, label='Poisson Distribution with $\\lambda$=2', alpha=0.5) \n", + "plt.xlabel('x') \n", + "plt.ylabel('P(X=x)') \n", + "plt.title('Poisson Distribution') \n", + "plt.legend() \n", + "plt.grid(True) \n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "1572d801-27ce-4e06-8fd9-1348c6db2e77", + "metadata": {}, + "source": [ + "**Question 1b:**
\n", + "i) n=20, p=0.23
\n", + "$\\lambda=np=4.6$" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "34cf4696-59b3-4938-a334-530fd3915fa1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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qJUtLSwDA7du34eTkVOfDbZx1IiKiSpSdc2RlZSVyJVQbZb+v+pwzxoBERERUDZ4H9GzRx++LAYmIiIhIgAGJiIiIyvn6669hZ2cndhmi4UnaREREdbA06fcGG1uj0aC4uBjm5uaQSCSY3PelBltXZSIiIjBgwACDr7exYEAiIiKiciwtLbXfCHse8RAbERGREerVqxeio6MRHR2Npk2bwtHRETNmzIBGowEA/Pe//8XIkSPRrFkzWFlZoX///rh8+bL29cJDbKdPn0bv3r1hY2MDW1tb+Pv748SJEwCAa9euYdCgQWjWrBmaNGmC9u3bY8+ePdrXHjx4EIGBgTA3N4eLiwumTp2KJ0+e6NT64Ycf4pNPPoG9vT3kcjlmzZrVsBNUDQYkIiIiI7Vp0yaYmJggPT0dy5YtQ3x8PNatWwcAGD16NE6cOIGffvoJqamp0Gg0GDBgQKVfjR82bBhatGiB48ePIyMjA1OnToWpqSkAYPz48SguLsahQ4fw22+/4fPPP4e1tTUA4ObNmxgwYAC6dOmC06dPY/Xq1Vi/fj3mzZtXrtYmTZogLS0NCxcuxJw5c5CUlNSAs1M1HmIjIsM6EKefcTRSAF7Ar/GARF2/sXrH6KUkosbG3d0dS5cuhUQiQdu2bfHbb79h6dKl6NWrF3766SccOXIEXbt2BQBs3rwZ7u7u2LlzJwYPHlxurKysLEyZMgVeXl4AAE9PT51l4eHh8PHxAQC0bt1au2zVqlVwd3fHihUrIJFI4OXlhezsbHz66aeYOXOm9kKYHTt2RGxsrHbsFStWIDk5GX379m2YyakG9yAREREZqZdfflnnmkBBQUG4fPkyzp8/DxMTEygUCu0yBwcHtG3bFhcuXKhwLKVSiXfffRfBwcFYsGABrly5ol324YcfYt68eejWrRtiY2Nx5swZ7bILFy4gKChIp45u3brh4cOHuHHjhratY8eOOutzcXHR3jJEDAxIREREVK1Zs2bh3LlzGDhwIPbv3w9vb2/8+OOPAIB3330Xf/75J0aMGIHffvsNAQEBWL58ea3GLztcV0YikUCtrufe4XpgQCIiIjJSaWlpOs+PHTsGT09PeHt748mTJzrL7927h0uXLsHb27vS8V566SVMnjwZe/fuxZtvvomNGzdql7m7u+P999/HDz/8gI8++ghfffUVAKBdu3bac5zKHDlyBDY2NmjRooW+NlXvGJCIiIiMVFZWFpRKJS5duoTvv/8ey5cvx8SJE+Hp6Yk33ngDUVFROHz4ME6fPo3hw4fDzc0Nb7zxRrlxHj9+jOjoaKSkpODatWs4cuQIjh8/jnbt2gEAJk2ahF9++QV//fUXMjMzceDAAe2ycePG4fr165gwYQIuXryIXbt2ITY2FkqlslHfiJcnaRMRERmpkSNH4vHjxwgMDIRMJsPEiRMxduxYAMDGjRsxceJEvPbaaygpKUGPHj2wZ8+ecoe6AEAmk+HevXsYOXIkcnNz4ejoiDfffBOzZ88GAJSWlmL8+PG4ceMGbG1t0a9fPyxduhQA4Obmhj179mDKlCnw9fWFvb09xowZg+nTpxtuIuqAAYmIiKgOGvLq1mq1GgUFBbC1ta3XXhZTU1MkJCRg9erV5ZY1a9YM33zzTaWvHT16NEaPHg0AMDMzw/fff19p3+rON+rZsyfS09MrXZ6SklKubefOnVWO2dAaxb6tlStXwsPDAxYWFlAoFFVO4ldffYVXXnkFzZo1Q7NmzRAcHFyuv0ajwcyZM+Hi4gJLS0sEBwfrXPwKAPLy8jBs2DDY2trCzs4OY8aMwcOHDxtk+4iIiOjZInpA2rZtG5RKJWJjY5GZmQlfX1+EhoZW+tW+lJQUDB06FAcOHEBqairc3d0REhKCmzdvavssXLgQX3zxBdasWYO0tDQ0adIEoaGhKCoq0vYZNmwYzp07h6SkJOzevRuHDh3S7nYkIiKi55voASk+Ph5RUVGIjIyEt7c31qxZAysrK2zYsKHC/ps3b8a4cePg5+cHLy8vrFu3Dmq1GsnJyQCe7j1KSEjA9OnT8cYbb6Bjx4745ptvkJ2drd1dd+HCBSQmJmLdunVQKBTo3r07li9fjq1btyI7O9tQm05ERNRgUlJSkJCQIHYZzyxRA1JJSQkyMjIQHBysbZNKpQgODkZqamqNxigsLIRKpYK9vT0A4K+//kJOTo7OmE2bNoVCodCOmZqaCjs7OwQEBGj7BAcHQyqVlvtKJBERET1/RD1J++7duygtLYWzs7NOu7OzMy5evFijMT799FO4urpqA1FOTo52DOGYZctycnLg5OSks9zExAT29vbaPkLFxcUoLi7WPi8oKAAAqFSqSu9bI7ayuhprfcaG811DGv38f5nq/4+j0sd4/J1V63l9f6tUKmg0GqjVaoNetLDsmkFl66baUavV0Gg0UKlUkMlkOstq+h5+pr/FtmDBAmzduhUpKSmwsLBo0HXFxcVpv874d3v37oWVlVWDrru+xLzZ3/OI810dL72OlvRQD98k+ttdx6lqz9v728TEBHK5HA8fPkRJSYnB1//gwQODr9MYlJSU4PHjxzh06BCePHmis6ywsLBGY4gakBwdHSGTyZCbm6vTnpubC7lcXuVrFy9ejAULFmDfvn06928pe11ubi5cXFx0xvTz89P2EZ4E/uTJE+Tl5VW63piYGCiVSu3zgoIC7Qnitra21W+sCFQqFZKSktC3b98Kr2tB+sX5rqFf4/UyjEojRdLDl9DX+neY1vdmta8oq+/znHte399FRUW4fv06rK2tG/x/xP9Oo9HgwYMHsLGx0bmHGdVMUVERLC0t0aNHj3K/t7IjQNURNSCZmZnB398fycnJCAsLAwDtCdfR0dGVvm7hwoWYP38+fvnlF53ziACgVatWkMvlSE5O1gaigoICpKWl4YMPPgDw9GZ9+fn5yMjIgL+/PwBg//79UKvVOjfu+ztzc3OYm5uXazc1NW30HxbPQo3GhPNdjfqGGQFTibr+AYm/rxp73t7fpaWlkEgkkEqlBr3qc9lhtbJ1U+1IpVJIJJIK3681ff+KfohNqVRi1KhRCAgIQGBgIBISEvDo0SNERkYCeHoVUDc3N8TFxQEAPv/8c8ycORNbtmyBh4eH9pwha2trWFtbQyKRYNKkSZg3bx48PT3RqlUrzJgxA66urtoQ1q5dO/Tr1w9RUVFYs2YNVCoVoqOjMWTIELi6uooyD0TUyB2IE7uC8nrHiF0BkdESPZZGRERg8eLFmDlzJvz8/HDq1CkkJiZqT7LOysrCrVu3tP1Xr16NkpISvPXWW3BxcdE+Fi9erO3zySefYMKECRg7diy6dOmChw8fIjExUWc32+bNm+Hl5YU+ffpgwIAB6N69O9auXWu4DSciImpAvXr1wqRJkypd7uHh0SguA5CSkgKJRIL8/Pwav6a6bdMH0fcgAUB0dHSlh9SElx+/evVqteNJJBLMmTMHc+bMqbSPvb09tmzZUpsyiYiI/qcB9ypKNBpYFBdDYm4OSCQNsrfw+PHjaNKkid7Hra2uXbvi1q1baNq0qdil6GgUAYmIiIgMq3nz5mKXAODp+cjVfTFLDKIfYiMiIqKG8eTJE0RHR6Np06ZwdHTEjBkztNdYEh5ik0gkWLduHf7xj3/AysoKnp6e+Omnn3TGO3jwIAIDA2Fubg4XFxdMnTpV52v0vXr1woQJEzBp0iQ0a9YMzs7O+Oqrr7TnFtvY2KBNmzb4z3/+o32N8BDbvXv3MHToULi5ucHKygo+Pj5V3ii3oTAgERERGalNmzbBxMQE6enpWLZsGeLj47Fu3bpK+8+ePRtvv/02zpw5gwEDBmDYsGHIy8sDANy8eRMDBgxAly5dcPr0aaxevRrr16/HvHnzyq3T0dER6enpmDBhAj744AMMHjwYXbt2RWZmJkJCQjBixIhKr0dUVFQEf39//Pzzzzh79izGjh2LESNGVHkj+4bAgERERGSk3N3dsXTpUrRt2xbDhg3DhAkTsHTp0kr7jx49GkOHDkWbNm3w2Wef4eHDh9pgsmrVKri7u2PFihXw8vJCWFgYZs+ejSVLluhc7dvX1xfTp0+Hp6cnYmJiYGFhAUdHR0RFRcHT0xMzZ87EvXv3cObMmQprcHNzw8cffww/Pz+0bt0aEyZMQL9+/bB9+3b9Tk41GJCIiIiM1Msvv6xzocmgoCBcvnwZpaWlFfb/+4WXmzRpAltbW+2FlS9cuICgoCCd8bp164aHDx/ixo0bFY4hk8ng4OAAHx8fbVvZt9SFF2wuU1pairlz58LHxwf29vawtrbGL7/8gqysrNpser3xJG0iIiICUP4iihKJpNb3gqtojL+3lQWsysZdtGgRli1bhoSEBPj4+KBJkyaYNGmSwW/1woBERERkpNLS0nSeHzt2DJ6enuVu4FoT7dq1w7/+9S9oNBptyDly5AhsbGzQokULvdRbNuYbb7yB4cOHA3gapH7//Xd4e3vrbR01wUNsRERERiorKwtKpRKXLl3C999/j+XLl2PixIl1GmvcuHG4fv06JkyYgIsXL2LXrl2IjY2FUqnU6+1QPD09kZSUhKNHj+LChQt47733yt2z1RC4B4mIiMhIjRw5Eo8fP0ZgYCBkMhkmTpyIsWPH1mksNzc37NmzB1OmTIGvry/s7e0xZswYTJ8+Xa81T58+HX/++SdCQ0NhZWWFsWPHIiwsDPfv39freqrDgERERFQXDXgvPI1ajaKCApjZ2kJSx70zf78TxerVq8stF96Zouz6SH8nvP1Hz549q/y6vfDuFxWtR7iuXr166Ty3t7fHzp07K11HZevRNx5iIyIiIhJgQCIiIiISYEAiIiIiEmBAIiIiIhJgQCIiIqpGRScwU+Olj98Xv8VGRAaV+uc9vYyjlsgAByD9ah6kmopvm1BTQb31UhIZobIrQBcWFsLS0lLkaqimym6EK7yqd20wIBEREVVCJpPBzs5Oe98wKysrnXuRNRS1Wo2SkhIUFRXp9SKMxk6j0aCwsBC3b9+GnZ1dna4YXoYBiYiIqApyuRxA5TdXbQgajQaPHz+GpaWlQQKZsbGzs9P+3uqKAYmIiKgKEokELi4ucHJygkqlMsg6VSoVDh06hB49etTrMNHzyNTUtF57jsowIBEREdWATCbTyx/emq7ryZMnsLCwYEASCQ9sEhEREQkwIBEREREJMCARERERCTAgEREREQkwIBEREREJMCARERERCTAgEREREQkwIBEREREJMCARERERCTAgEREREQkwIBEREREJMCARERERCYgekFauXAkPDw9YWFhAoVAgPT290r7nzp1DeHg4PDw8IJFIkJCQUK5P2TLhY/z48do+vXr1Krf8/fffb4jNIyIiomeQqAFp27ZtUCqViI2NRWZmJnx9fREaGorbt29X2L+wsBCtW7fGggULIJfLK+xz/Phx3Lp1S/tISkoCAAwePFinX1RUlE6/hQsX6nfjiIiI6JklakCKj49HVFQUIiMj4e3tjTVr1sDKygobNmyosH+XLl2waNEiDBkyBObm5hX2ad68OeRyufaxe/duvPjii+jZs6dOPysrK51+tra2et8+IiIiejaZiLXikpISZGRkICYmRtsmlUoRHByM1NRUva3ju+++g1KphEQi0Vm2efNmfPfdd5DL5Rg0aBBmzJgBKyurSscqLi5GcXGx9nlBQQEAQKVSQaVS6aVefSurq7HWZ2w43zWjlsj0Oo4+xqvR70wj+hkJ5Rnwvcb3t2FxvhtOTedUtIB09+5dlJaWwtnZWafd2dkZFy9e1Ms6du7cifz8fIwePVqn/Z133kHLli3h6uqKM2fO4NNPP8WlS5fwww8/VDpWXFwcZs+eXa597969VQarxqDsMCMZBue7Gg5d9Tpcnr2i3mPs2bOnBr286r0evatR3frF97dhcb71r7CwsEb9RAtIhrB+/Xr0798frq6uOu1jx47V/uzj4wMXFxf06dMHV65cwYsvvljhWDExMVAqldrnBQUFcHd3R0hISKM9PKdSqZCUlIS+ffvC1NRU7HKMHue7ZtK/na6XcdQSGfLsFbDPS4NUU1qvsQJHzKu+06/x9VpHg3hFWX0fPeH727A43w2n7AhQdUQLSI6OjpDJZMjNzdVpz83NrfQE7Nq4du0a9u3bV+VeoTIKxdP/A/3jjz8qDUjm5uYVnvdkamra6N+8z0KNxoTzXbX6hpmKxqvvmDX6fUnU9VpHgxDhfcb3t2FxvvWvpvMp2kF1MzMz+Pv7Izk5WdumVquRnJyMoKCgeo+/ceNGODk5YeDAgdX2PXXqFADAxcWl3uslIiKiZ5+oh9iUSiVGjRqFgIAABAYGIiEhAY8ePUJkZCQAYOTIkXBzc0NcXByApyddnz9/XvvzzZs3cerUKVhbW6NNmzbacdVqNTZu3IhRo0bBxER3E69cuYItW7ZgwIABcHBwwJkzZzB58mT06NEDHTt2NNCWE9GzJvXPe2KXUE5Qb7ErIDJeogakiIgI3LlzBzNnzkROTg78/PyQmJioPXE7KysLUun/dnJlZ2ejU6dO2ueLFy/G4sWL0bNnT6SkpGjb9+3bh6ysLPzf//1fuXWamZlh37592jDm7u6O8PBwTJ+un/MiiIiI6Nkn+kna0dHRiI6OrnDZ30MP8PQq2RqNptoxQ0JCKu3n7u6OgwcP1rpOIiIien40wgt7EBEREYmLAYmIiIhIgAGJiIiISIABiYiIiEiAAYmIiIhIgAGJiIiISIABiYiIiEiAAYmIiIhIgAGJiIiISIABiYiIiEiAAYmIiIhIgAGJiIiISIABiYiIiEjAROwCiKhuUtd/LHYJ5QSNWSx2CUREesE9SEREREQCDEhEREREAgxIRERERAIMSEREREQCDEhEREREAgxIRERERAIMSEREREQCDEhEREREAgxIRERERAIMSEREREQCDEhEREREAgxIRERERAIMSEREREQCDEhEREREAgxIRERERAIMSEREREQCDEhEREREAqIHpJUrV8LDwwMWFhZQKBRIT0+vtO+5c+cQHh4ODw8PSCQSJCQklOsza9YsSCQSnYeXl5dOn6KiIowfPx4ODg6wtrZGeHg4cnNz9b1pRERE9IwSNSBt27YNSqUSsbGxyMzMhK+vL0JDQ3H79u0K+xcWFqJ169ZYsGAB5HJ5peO2b98et27d0j4OHz6ss3zy5Mn497//jR07duDgwYPIzs7Gm2++qddtIyIiomeXqAEpPj4eUVFRiIyMhLe3N9asWQMrKyts2LChwv5dunTBokWLMGTIEJibm1c6romJCeRyufbh6OioXXb//n2sX78e8fHxePXVV+Hv74+NGzfi6NGjOHbsmN63kYiIiJ49ogWkkpISZGRkIDg4+H/FSKUIDg5Gampqvca+fPkyXF1d0bp1awwbNgxZWVnaZRkZGVCpVDrr9fLywgsvvFDv9RIREZFxMBFrxXfv3kVpaSmcnZ112p2dnXHx4sU6j6tQKPD111+jbdu2uHXrFmbPno1XXnkFZ8+ehY2NDXJycmBmZgY7O7ty683Jyal03OLiYhQXF2ufFxQUAABUKhVUKlWd621IZXU11vqMjaHnWy2RGWQ9tVGTbddX3WXj6GM8Q9atT4b8t83PE8PifDecms6paAGpofTv31/7c8eOHaFQKNCyZUts374dY8aMqfO4cXFxmD17drn2vXv3wsrKqs7jGkJSUpLYJTxXDDbfDl0Ns55a2LNnT/Wd9Fx3nr2i3mOIUbc+1KhuPePniWFxvvWvsLCwRv1EC0iOjo6QyWTlvj2Wm5tb5QnYtWVnZ4eXXnoJf/zxBwBALpejpKQE+fn5OnuRqltvTEwMlEql9nlBQQHc3d0REhICW1tbvdWrTyqVCklJSejbty9MTU3FLsfoGXq+07+d3uDrqK3AEfOq7aOvutUSGfLsFbDPS4NUU1qvsQxZtz7VpG594eeJYXG+G07ZEaDqiBaQzMzM4O/vj+TkZISFhQEA1Go1kpOTER0drbf1PHz4EFeuXMGIESMAAP7+/jA1NUVycjLCw8MBAJcuXUJWVhaCgoIqHcfc3LzCE8NNTU0b/Zv3WajRmBhqvusbChpCTbZb33VLNaX1HlOMuvVBjH/X/DwxLM63/tV0PkU9xKZUKjFq1CgEBAQgMDAQCQkJePToESIjIwEAI0eOhJubG+Li4gA8PbH7/Pnz2p9v3ryJU6dOwdraGm3atAEAfPzxxxg0aBBatmyJ7OxsxMbGQiaTYejQoQCApk2bYsyYMVAqlbC3t4etrS0mTJiAoKAgvPzyyyLMAhFRAzoQp59xNFIAXsCv8YBEXb+xesfopSSihiRqQIqIiMCdO3cwc+ZM5OTkwM/PD4mJidoTt7OysiCV/u+LdtnZ2ejUqZP2+eLFi7F48WL07NkTKSkpAIAbN25g6NChuHfvHpo3b47u3bvj2LFjaN68ufZ1S5cuhVQqRXh4OIqLixEaGopVq1YZZqOJiIio0RP9JO3o6OhKD6mVhZ4yHh4e0Gg0VY63devWatdpYWGBlStXYuXKlTWuk4iIiJ4fot9qhIiIiKixYUAiIiIiEmBAIiIiIhJgQCIiIiISYEAiIiIiEmBAIiIiIhJgQCIiIiISYEAiIiIiEmBAIiIiIhJgQCIiIiISYEAiIiIiEmBAIiIiIhJgQCIiIiISYEAiIiIiEmBAIiIiIhJgQCIiIiISYEAiIiIiEmBAIiIiIhJgQCIiIiISYEAiIiIiEmBAIiIiIhJgQCIiIiISYEAiIiIiEmBAIiIiIhIwEbsAIiJqOKl/3tPLOGqJDHAA0q/mQaoprddYQb31UhJRg+IeJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIB0QPSypUr4eHhAQsLCygUCqSnp1fa99y5cwgPD4eHhwckEgkSEhLK9YmLi0OXLl1gY2MDJycnhIWF4dKlSzp9evXqBYlEovN4//339b1pRERE9IwSNSBt27YNSqUSsbGxyMzMhK+vL0JDQ3H79u0K+xcWFqJ169ZYsGAB5HJ5hX0OHjyI8ePH49ixY0hKSoJKpUJISAgePXqk0y8qKgq3bt3SPhYuXKj37SMiIqJnk6hX0o6Pj0dUVBQiIyMBAGvWrMHPP/+MDRs2YOrUqeX6d+nSBV26dAGACpcDQGJios7zr7/+Gk5OTsjIyECPHj207VZWVpWGLCIiInq+iRaQSkpKkJGRgZiYGG2bVCpFcHAwUlNT9bae+/fvAwDs7e112jdv3ozvvvsOcrkcgwYNwowZM2BlZVXpOMXFxSguLtY+LygoAACoVCqoVCq91atPZXU11vqMjaHnWy2RGWQ9tVGTbddX3WXj6GM8Q9atT8Y83887fn43nJrOqUSj0WgauJYKZWdnw83NDUePHkVQUJC2/ZNPPsHBgweRlpZW5es9PDwwadIkTJo0qdI+arUar7/+OvLz83H48GFt+9q1a9GyZUu4urrizJkz+PTTTxEYGIgffvih0rFmzZqF2bNnl2vfsmVLlcGKiIiIGo/CwkK88847uH//PmxtbSvtZ9Q3qx0/fjzOnj2rE44AYOzYsdqffXx84OLigj59+uDKlSt48cUXKxwrJiYGSqVS+7ygoADu7u4ICQmpcoLFpFKpkJSUhL59+8LU1FTscoyeoec7/dvpDb6O2gocMa/aPvqqWy2RIc9eAfu8tHrfPNWQdeuTMc/3846f3w2n7AhQdUQLSI6OjpDJZMjNzdVpz83N1cu5QdHR0di9ezcOHTqEFi1aVNlXoVAAAP74449KA5K5uTnMzc3LtZuamjb6N++zUKMxMdR81/ePVEOoyXbru26pprTeY4pRtz4Y83zTU/z81r+azqdo32IzMzODv78/kpOTtW1qtRrJyck6h9xqS6PRIDo6Gj/++CP279+PVq1aVfuaU6dOAQBcXFzqvF4iIiIyHqIeYlMqlRg1ahQCAgIQGBiIhIQEPHr0SPuttpEjR8LNzQ1xcXEAnp7Yff78ee3PN2/exKlTp2BtbY02bdoAeHpYbcuWLdi1axdsbGyQk5MDAGjatCksLS1x5coVbNmyBQMGDICDgwPOnDmDyZMno0ePHujYsaMIs0BERESNjagBKSIiAnfu3MHMmTORk5MDPz8/JCYmwtnZGQCQlZUFqfR/O7mys7PRqVMn7fPFixdj8eLF6NmzJ1JSUgAAq1evBvD0YpB/t3HjRowePRpmZmbYt2+fNoy5u7sjPDwc06c3vvMLiIiISByin6QdHR2N6OjoCpeVhZ4yHh4eqO5Ld9Utd3d3x8GDB2tVIxERET1f6hyQiouLkZaWhmvXrqGwsBDNmzdHp06danTODxEREVFjVuuAdOTIESxbtgz//ve/oVKptOf25OXlobi4GK1bt8bYsWPx/vvvw8bGpiFqJiIiImpQtfoW2+uvv46IiAh4eHhg7969ePDgAe7du4cbN26gsLAQly9fxvTp05GcnIyXXnoJSUlJDVU3ERERUYOp1R6kgQMH4l//+lel1xBo3bo1WrdujVGjRuH8+fO4deuWXookIiIiMqRaBaT33nuvxn29vb3h7e1d64KIiIiIxFbnC0UeOHCg0mVffvllXYclIiIiEl2dA1K/fv0wZcoUnbvi3r17F4MGDcLUqVP1UhwRERGRGOq1B+nHH39Ely5dcP78efz888/o0KEDCgoKtLfuICIiInoW1Tkgde3aFadOnUKHDh3QuXNn/OMf/8DkyZORkpKCli1b6rNGIiIiIoOq181qf//9d5w4cQItWrSAiYkJLl26hMLCQn3VRkRERCSKOgekBQsWICgoCH379sXZs2eRnp6OkydPomPHjkhNTdVnjUREREQGVeeAtGzZMuzcuRPLly+HhYUFOnTogPT0dLz55pvlbhRLRERE9Cyp873YfvvtNzg6Ouq0mZqaYtGiRXjttdfqXRgRERGRWOq8B0kYjv6uZ8+edR2WiIiISHT1Okl7wYIFyM/PL/czERER0bOsXgHps88+Q15eXrmfiYiIiJ5l9QpIGo2mwp+JiIiInmX1CkhERERExogBiYiIiEiAAYmIiIhIgAGJiIiISEBvAUkikehrKCIiIiJR6S0g8VtsREREZCzqfKsRADh//jzc3Ny0P7u6uuqlKCIiIiIx1Ssgubu7V/gzERER0bOs1gFp/fr1GDNmTKXLHzx4gMmTJ2PdunX1KozIUJYm/a6XcSSaUrQCsPLAH9BIZPUaa3Lfl/RSExER1U2tz0FSKpV47bXXkJOTU27ZL7/8gvbt2+P48eN6KY6IiIhIDLUOSKdPn8ajR4/Qvn17fP/99wCe7jUaM2YMBg0ahOHDh+PEiRN6L5SIiIjIUGp9iM3DwwMHDhxAQkICoqKisHnzZvz222+wtrbGkSNH0KVLl4aok4iIiMhg6nyS9nvvvYdDhw5h586daNKkCXbv3g0fHx991kZEREQkijpdB+nIkSPw9fXFxYsXkZiYiP79+yMoKAjLli3Td31EREREBlfrgPTRRx/h1VdfxaBBg5CZmYmQkBBs374d69evx7x589CrVy/89ddfNR5v5cqV8PDwgIWFBRQKBdLT0yvte+7cOYSHh8PDwwMSiQQJCQl1GrOoqAjjx4+Hg4MDrK2tER4ejtzc3BrXTERERMat1gFp165d2LdvH5YsWQILCwtte0REBM6ePYumTZuiY8eONRpr27ZtUCqViI2NRWZmJnx9fREaGorbt29X2L+wsBCtW7fGggULIJfL6zzm5MmT8e9//xs7duzAwYMHkZ2djTfffLMWs0BERETGrNYB6cyZM3jllVcqXObs7Ixdu3Zh1apVNRorPj4eUVFRiIyMhLe3N9asWQMrKyts2LChwv5dunTBokWLMGTIEJibm9dpzPv372P9+vWIj4/Hq6++Cn9/f2zcuBFHjx7FsWPHalQ3ERERGbdaByQrK6tq+4wYMaLaPiUlJcjIyEBwcPD/ipFKERwcjNTU1NqWVeMxMzIyoFKpdPp4eXnhhRdeqPN6iYiIyLjU6ltsCxYswIcfflijkJSWloa7d+9i4MCBFS6/e/cuSktL4ezsrNPu7OyMixcv1qasWo2Zk5MDMzMz2NnZletT0cUvyxQXF6O4uFj7vKCgAACgUqmgUqnqVG9DK6ursdbXWEg0pXodRx/j1eR3pq7n1bobgiHrLhtHH+Nxvqtn6Pl+3vHzu+HUdE5rFZDOnz+Pli1bYvDgwRg0aBACAgLQvHlzAMCTJ09w/vx5HD58GN999x2ys7PxzTff1L7yRiouLg6zZ88u1753794aBUYxJSUliV1Co9ZKz+N5FF2p9xh79tTg9icOXeu9Hn3bs2dP9Z30XHeevaLeY4hRtz4Y9XwTAH5+N4TCwsIa9atVQPrmm29w+vRprFixAu+88w4KCgogk8lgbm6uXWGnTp3w7rvvYvTo0ToncQs5OjpCJpOV+/ZYbm5upSdgV6cmY8rlcpSUlCA/P19nL1J1642JiYFSqdQ+LygogLu7O0JCQmBra1unehuaSqVCUlIS+vbtC1NTU7HLabRWHvhDL+NINKXwKLqCqxYv1vtebON7t6m2T/q30+u1joYQOGJetX30VbdaIkOevQL2eWmQ1nOvnSHr1idjnu/nHT+/G07ZEaDq1PpCkb6+vvjqq6/w5Zdf4syZM7h27RoeP34MR0dH+Pn5wdHRsUbjmJmZwd/fH8nJyQgLCwMAqNVqJCcnIzo6urZl1XhMf39/mJqaIjk5GeHh4QCAS5cuISsrC0FBQZWObW5uXuGJ4aampo3+zfss1Cim+oaZisar75g1+X3V949UQxCjbqmmtN5jcr5rzlDzTU/x81v/ajqftQ5IarUaixYtwk8//YSSkhL06dMHsbGxsLS0rHWRSqUSo0aNQkBAAAIDA5GQkIBHjx4hMjISADBy5Ei4ubkhLi4OwNOTsM+fP6/9+ebNmzh16hSsra3Rpk2bGo3ZtGlTjBkzBkqlEvb29rC1tcWECRMQFBSEl19+udbbQERERMan1gFp/vz5mDVrFoKDg2FpaYlly5bh9u3blX41vyoRERG4c+cOZs6ciZycHPj5+SExMVF7knVWVhak0v990S47OxudOnXSPl+8eDEWL16Mnj17IiUlpUZjAsDSpUshlUoRHh6O4uJihIaG1vjSBERERGT8ah2QvvnmG6xatQrvvfceAGDfvn0YOHAg1q1bpxNmaio6OrrSQ2ploaeMh4cHNBpNvcYEAAsLC6xcuRIrV66sVa1ERET0fKh1osnKysKAAQO0z4ODgyGRSJCdna3XwoiIiIjEUuuA9OTJk3LfTjM1NeW1GoiIiMho1PoQm0ajwejRo3W+0VVUVIT3338fTZo00bb98MMP+qmQiIiIyMBqHZBGjRpVrm348OF6KYaIiIioMah1QNq4cWND1EFERETUaNT+a2dERERERo4BiYiIiEiAAYmIiIhIgAGJiIiISKDWJ2kTGZuXs9bqZRy1RIa7Dl3R5cbXerhB6GK91ERERHXDPUhEREREAgxIRERERAIMSEREREQCDEhEREREAjxJm4iIGp8DcWJXUF7vGLErIAPiHiQiIiIiAe5BIiKiRif1z3til1BOUG+xKyBD4h4kIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIigUYRkFauXAkPDw9YWFhAoVAgPT29yv47duyAl5cXLCws4OPjgz179ugsl0gkFT4WLVqk7ePh4VFu+YIFCxpk+4iIiOjZInpA2rZtG5RKJWJjY5GZmQlfX1+Ehobi9u3bFfY/evQohg4dijFjxuDkyZMICwtDWFgYzp49q+1z69YtnceGDRsgkUgQHh6uM9acOXN0+k2YMKFBt5WIiIieDaIHpPj4eERFRSEyMhLe3t5Ys2YNrKyssGHDhgr7L1u2DP369cOUKVPQrl07zJ07F507d8aKFSu0feRyuc5j165d6N27N1q3bq0zlo2NjU6/Jk2aNOi2EhER0bPBRMyVl5SUICMjAzExMdo2qVSK4OBgpKamVvia1NRUKJVKnbbQ0FDs3Lmzwv65ubn4+eefsWnTpnLLFixYgLlz5+KFF17AO++8g8mTJ8PEpOIpKS4uRnFxsfZ5QUEBAEClUkGlUlW5nWIpq6ux1tdYqCUyvY6jj/Fq8jvTV936ZMi6Od+cb0Mz5GcpP78bTk3nVNSAdPfuXZSWlsLZ2Vmn3dnZGRcvXqzwNTk5ORX2z8nJqbD/pk2bYGNjgzfffFOn/cMPP0Tnzp1hb2+Po0ePIiYmBrdu3UJ8fHyF48TFxWH27Nnl2vfu3QsrK6tKt7ExSEpKEruExs2hq16Hy7NX1HsM4Xl1FdJz3fogRt2c72pwvvWmRnXrGT+/9a+wsLBG/UQNSIawYcMGDBs2DBYWFjrtf98L1bFjR5iZmeG9995DXFwczM3Ny40TExOj85qCggK4u7sjJCQEtra2DbcB9aBSqZCUlIS+ffvC1NRU7HIarfRvp+tlHLVEhjx7Bezz0iDVlNZrrMAR86rto6+69cmQdXO+Od+GVpO69YWf3w2n7AhQdUQNSI6OjpDJZMjNzdVpz83NhVwur/A1crm8xv1//fVXXLp0Cdu2bau2FoVCgSdPnuDq1ato27ZtueXm5uYVBidTU9NG/+Z9FmoUU30/7Csar75j1uT3pe+69UGMujnfVeN8648Yn6P8/Na/ms6nqCdpm5mZwd/fH8nJydo2tVqN5ORkBAUFVfiaoKAgnf7A012QFfVfv349/P394evrW20tp06dglQqhZOTUy23goiIiIyN6IfYlEolRo0ahYCAAAQGBiIhIQGPHj1CZGQkAGDkyJFwc3NDXFwcAGDixIno2bMnlixZgoEDB2Lr1q04ceIE1q5dqzNuQUEBduzYgSVLlpRbZ2pqKtLS0tC7d2/Y2NggNTUVkydPxvDhw9GsWbOG32giIiJq1EQPSBEREbhz5w5mzpyJnJwc+Pn5ITExUXsidlZWFqTS/+3o6tq1K7Zs2YLp06dj2rRp8PT0xM6dO9GhQwedcbdu3QqNRoOhQ4eWW6e5uTm2bt2KWbNmobi4GK1atcLkyZPLfTuOiIiInk+iByQAiI6ORnR0dIXLUlJSyrUNHjwYgwcPrnLMsWPHYuzYsRUu69y5M44dO1brOomIiOj5IPqFIomIiIgaGwYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIigUYRkFauXAkPDw9YWFhAoVAgPT29yv47duyAl5cXLCws4OPjgz179ugsHz16NCQSic6jX79+On3y8vIwbNgw2Nraws7ODmPGjMHDhw/1vm1ERET07BE9IG3btg1KpRKxsbHIzMyEr68vQkNDcfv27Qr7Hz16FEOHDsWYMWNw8uRJhIWFISwsDGfPntXp169fP9y6dUv7+P7773WWDxs2DOfOnUNSUhJ2796NQ4cOYezYsQ22nURERPTsED0gxcfHIyoqCpGRkfD29saaNWtgZWWFDRs2VNh/2bJl6NevH6ZMmYJ27dph7ty56Ny5M1asWKHTz9zcHHK5XPto1qyZdtmFCxeQmJiIdevWQaFQoHv37li+fDm2bt2K7OzsBt1eIiIiavxEDUglJSXIyMhAcHCwtk0qlSI4OBipqakVviY1NVWnPwCEhoaW65+SkgInJye0bdsWH3zwAe7du6czhp2dHQICArRtwcHBkEqlSEtL08emERER0TPMRMyV3717F6WlpXB2dtZpd3Z2xsWLFyt8TU5OToX9c3JytM/79euHN998E61atcKVK1cwbdo09O/fH6mpqZDJZMjJyYGTk5POGCYmJrC3t9cZ5++Ki4tRXFysfV5QUAAAUKlUUKlUNd9oAyqrq7HW11ioJTK9jqOP8WryO9NX3fpkyLo535xvQzPkZyk/vxtOTedU1IDUUIYMGaL92cfHBx07dsSLL76IlJQU9OnTp05jxsXFYfbs2eXa9+7dCysrqzrXaghJSUlil9C4OXTV63B59op6jyH84kGF9Fy3PohRN+e7GpxvvalR3XrGz2/9KywsrFE/UQOSo6MjZDIZcnNzddpzc3Mhl8srfI1cLq9VfwBo3bo1HB0d8ccff6BPnz6Qy+XlTgJ/8uQJ8vLyKh0nJiYGSqVS+7ygoADu7u4ICQmBra1tldspFpVKhaSkJPTt2xempqZil9NopX87XS/jqCUy5NkrYJ+XBqmmtF5jBY6YV20ffdWtT4asm/PN+Ta0mtS98sAfelmXRFMKj6IruGrxIjT13Js2vncbvdRkLMqOAFVH1IBkZmYGf39/JCcnIywsDACgVquRnJyM6OjoCl8TFBSE5ORkTJo0SduWlJSEoKCgStdz48YN3Lt3Dy4uLtox8vPzkZGRAX9/fwDA/v37oVaroVBU/H9H5ubmMDc3L9duamra6MPHs1CjmOr7YV/RePUdsya/L33XrQ9i1M35rhrnW39qUnd9w0xF49V3TH7+66rpfIj+LTalUomvvvoKmzZtwoULF/DBBx/g0aNHiIyMBACMHDkSMTEx2v4TJ05EYmIilixZgosXL2LWrFk4ceKENlA9fPgQU6ZMwbFjx3D16lUkJyfjjTfeQJs2bRAaGgoAaNeuHfr164eoqCikp6fjyJEjiI6OxpAhQ+Dq6mr4SSAiIqJGRfRzkCIiInDnzh3MnDkTOTk58PPzQ2JiovZE7KysLEil/8txXbt2xZYtWzB9+nRMmzYNnp6e2LlzJzp06AAAkMlkOHPmDDZt2oT8/Hy4uroiJCQEc+fO1dkDtHnzZkRHR6NPnz6QSqUIDw/HF198YdiNJyIiokZJ9IAEANHR0ZUeUktJSSnXNnjwYAwePLjC/paWlvjll1+qXae9vT22bNlSqzqJiIjo+dAoAhIZh6VJv4tdQjmT+74kdglERPQMEv0cJCIiIqLGhgGJiIiISIABiYiIiEiAAYmIiIhIgAGJiIiISIDfYiMiItKTl7PW6mUctUSGuw5d0eXG13q4qvhivdT0vOEeJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAROxCyDj8XLWWrFLqMBisQsgIqJnEPcgEREREQkwIBEREREJMCARERERCTAgEREREQkwIBEREREJMCARERERCTAgEREREQk0ioC0cuVKeHh4wMLCAgqFAunp6VX237FjB7y8vGBhYQEfHx/s2bNHu0ylUuHTTz+Fj48PmjRpAldXV4wcORLZ2dk6Y3h4eEAikeg8FixY0CDbR0RERM8W0QPStm3boFQqERsbi8zMTPj6+iI0NBS3b9+usP/Ro0cxdOhQjBkzBidPnkRYWBjCwsJw9uxZAEBhYSEyMzMxY8YMZGZm4ocffsClS5fw+uuvlxtrzpw5uHXrlvYxYcKEBt1WIiIiejaIHpDi4+MRFRWFyMhIeHt7Y82aNbCyssKGDRsq7L9s2TL069cPU6ZMQbt27TB37lx07twZK1asAAA0bdoUSUlJePvtt9G2bVu8/PLLWLFiBTIyMpCVlaUzlo2NDeRyufbRpEmTBt9eIiIiavxEvdVISUkJMjIyEBMTo22TSqUIDg5Gampqha9JTU2FUqnUaQsNDcXOnTsrXc/9+/chkUhgZ2en075gwQLMnTsXL7zwAt555x1MnjwZJiYVT0lxcTGKi4u1zwsKCgA8PaSnUqmq2kzRlNVlqPrUEplB1lMbNdl2fdVdNo4+xjNk3frE+TYszrdhGfN8rzzwR73Xo2/je7dpkHFr+jdRotFoNA1SQQ1kZ2fDzc0NR48eRVBQkLb9k08+wcGDB5GWllbuNWZmZti0aROGDh2qbVu1ahVmz56N3Nzccv2LiorQrVs3eHl5YfPmzdr2+Ph4dO7cGfb29jh69ChiYmIQGRmJ+Pj4CmudNWsWZs+eXa59y5YtsLKyqtV2ExERkTgKCwvxzjvv4P79+7C1ta20n1HfrFalUuHtt9+GRqPB6tWrdZb9fS9Ux44dYWZmhvfeew9xcXEwNzcvN1ZMTIzOawoKCuDu7o6QkJAqJ1hMKpUKSUlJ6Nu3L0xNTRt8fenfTm/wddRW4Ih51fbRV91qiQx59grY56VBqimt11iGrFufON+Gxfk2LGOe7+dpD1LZEaDqiBqQHB0dIZPJyu35yc3NhVwur/A1crm8Rv3LwtG1a9ewf//+akOMQqHAkydPcPXqVbRt27bccnNz8wqDk6mpqUHCR30Yqsb6/iNuCDXZbn3XLdWU1ntMMerWB863YXG+DcuY51vTCA9pNtTfrZqOK+pJ2mZmZvD390dycrK2Ta1WIzk5WeeQ298FBQXp9AeApKQknf5l4ejy5cvYt28fHBwcqq3l1KlTkEqlcHJyquPWEBERkbEQ/RCbUqnEqFGjEBAQgMDAQCQkJODRo0eIjIwEAIwcORJubm6Ii4sDAEycOBE9e/bEkiVLMHDgQGzduhUnTpzA2rVrATwNR2+99RYyMzOxe/dulJaWIicnBwBgb28PMzMzpKamIi0tDb1794aNjQ1SU1MxefJkDB8+HM2aNRNnIoiIiKjRED0gRURE4M6dO5g5cyZycnLg5+eHxMREODs7AwCysrIglf5vR1fXrl2xZcsWTJ8+HdOmTYOnpyd27tyJDh06AABu3ryJn376CQDg5+ens64DBw6gV69eMDc3x9atWzFr1iwUFxejVatWmDx5crlvxxEREdHzSfSABADR0dGIjo6ucFlKSkq5tsGDB2Pw4MEV9vfw8EB1X8zr3Lkzjh07Vus6iYiI6Pkg+oUiiYiIiBobBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiKBRnEdJCIiIhLPy1lrxS6hAotFXTv3IBEREREJMCARERERCTAgEREREQkwIBEREREJMCARERERCTAgEREREQkwIBEREREJMCARERERCTAgEREREQkwIBEREREJMCARERERCfBebI3Q0qTf9TKORFOKVgBWHvgDGomsXmNN7vuSXmoiIiJ6FnAPEhEREZEAAxIRERGRAAMSERERkQADEhEREZEAAxIRERGRAAMSERERkQADEhEREZEAr4PUCL2ctVYv46glMtx16IouN76GVFNaz9EW66UmIiKiZwH3IBEREREJMCARERERCTAgEREREQk0ioC0cuVKeHh4wMLCAgqFAunp6VX237FjB7y8vGBhYQEfHx/s2bNHZ7lGo8HMmTPh4uICS0tLBAcH4/Llyzp98vLyMGzYMNja2sLOzg5jxozBw4cP9b5tRERE9OwRPSBt27YNSqUSsbGxyMzMhK+vL0JDQ3H79u0K+x89ehRDhw7FmDFjcPLkSYSFhSEsLAxnz57V9lm4cCG++OILrFmzBmlpaWjSpAlCQ0NRVFSk7TNs2DCcO3cOSUlJ2L17Nw4dOoSxY8c2+PYSERFR4yd6QIqPj0dUVBQiIyPh7e2NNWvWwMrKChs2bKiw/7Jly9CvXz9MmTIF7dq1w9y5c9G5c2esWLECwNO9RwkJCZg+fTreeOMNdOzYEd988w2ys7Oxc+dOAMCFCxeQmJiIdevWQaFQoHv37li+fDm2bt2K7OxsQ206ERERNVKiBqSSkhJkZGQgODhY2yaVShEcHIzU1NQKX5OamqrTHwBCQ0O1/f/66y/k5OTo9GnatCkUCoW2T2pqKuzs7BAQEKDtExwcDKlUirS0NL1tHxERET2bRL0O0t27d1FaWgpnZ2eddmdnZ1y8eLHC1+Tk5FTYPycnR7u8rK2qPk5OTjrLTUxMYG9vr+0jVFxcjOLiYu3z+/fvA3h6LpNKpapyO2vrQdETvYyjlmhQWFiIB0VP6n0dpHv37lXbR19165Mh6+Z8c74NjfNtWJxvw6pJ3XXx4MEDAE+POFWFF4qsobi4OMyePbtce6tWrUSoRgTRy8SuoG5Yt2GxbsNi3YbFug2rget+8OABmjZtWulyUQOSo6MjZDIZcnNzddpzc3Mhl8srfI1cLq+yf9l/c3Nz4eLiotPHz89P20d4EviTJ0+Ql5dX6XpjYmKgVCq1z9VqNfLy8uDg4ACJRFKDrTW8goICuLu74/r167C1tRW7HKPH+TYszrdhcb4Ni/PdcDQaDR48eABXV9cq+4kakMzMzODv74/k5GSEhYUBeBo8kpOTER0dXeFrgoKCkJycjEmTJmnbkpKSEBQUBODpHh25XI7k5GRtICooKEBaWho++OAD7Rj5+fnIyMiAv78/AGD//v1Qq9VQKBQVrtfc3Bzm5uY6bXZ2dnXccsOytbXlPzAD4nwbFufbsDjfhsX5bhhV7TkqI/ohNqVSiVGjRiEgIACBgYFISEjAo0ePEBkZCQAYOXIk3NzcEBcXBwCYOHEievbsiSVLlmDgwIHYunUrTpw4gbVrn96/TCKRYNKkSZg3bx48PT3RqlUrzJgxA66urtoQ1q5dO/Tr1w9RUVFYs2YNVCoVoqOjMWTIkGoTJRERERk/0QNSREQE7ty5g5kzZyInJwd+fn5ITEzUnmSdlZUFqfR/X7br2rUrtmzZgunTp2PatGnw9PTEzp070aFDB22fTz75BI8ePcLYsWORn5+P7t27IzExERYWFto+mzdvRnR0NPr06QOpVIrw8HB88cUXhttwIiIiarQkmupO46ZnVnFxMeLi4hATE1Pu8CDpH+fbsDjfhsX5NizOt/gYkIiIiIgERL+SNhEREVFjw4BEREREJMCARERERCTAgEREREQkwIBkpFauXAkPDw9YWFhAoVAgPT1d7JKMUlxcHLp06QIbGxs4OTkhLCwMly5dErus58aCBQu01z6jhnHz5k0MHz4cDg4OsLS0hI+PD06cOCF2WUaptLQUM2bMQKtWrWBpaYkXX3wRc+fOrfaeYdQwGJCM0LZt26BUKhEbG4vMzEz4+voiNDS03O1VqP4OHjyI8ePH49ixY0hKSoJKpUJISAgePXokdmlG7/jx4/jyyy/RsWNHsUsxWv/973/RrVs3mJqa4j//+Q/Onz+PJUuWoFmzZmKXZpQ+//xzrF69GitWrMCFCxfw+eefY+HChVi+fLnYpT2X+DV/I6RQKNClSxesWLECwNPbt7i7u2PChAmYOnWqyNUZtzt37sDJyQkHDx5Ejx49xC7HaD18+BCdO3fGqlWrMG/ePPj5+SEhIUHssozO1KlTceTIEfz6669il/JceO211+Ds7Iz169dr28LDw2FpaYnvvvtOxMqeT9yDZGRKSkqQkZGB4OBgbZtUKkVwcDBSU1NFrOz5cP/+fQCAvb29yJUYt/Hjx2PgwIE673PSv59++gkBAQEYPHgwnJyc0KlTJ3z11Vdil2W0unbtiuTkZPz+++8AgNOnT+Pw4cPo37+/yJU9n0S/1Qjp1927d1FaWqq9VUsZZ2dnXLx4UaSqng9qtRqTJk1Ct27ddG59Q/q1detWZGZm4vjx42KXYvT+/PNPrF69GkqlEtOmTcPx48fx4YcfwszMDKNGjRK7PKMzdepUFBQUwMvLCzKZDKWlpZg/fz6GDRsmdmnPJQYkIj0ZP348zp49i8OHD4tditG6fv06Jk6ciKSkJJ17K1LDUKvVCAgIwGeffQYA6NSpE86ePYs1a9YwIDWA7du3Y/PmzdiyZQvat2+PU6dOYdKkSXB1deV8i4ABycg4OjpCJpMhNzdXpz03NxdyuVykqoxfdHQ0du/ejUOHDqFFixZil2O0MjIycPv2bXTu3FnbVlpaikOHDmHFihUoLi6GTCYTsULj4uLiAm9vb522du3a4V//+pdIFRm3KVOmYOrUqRgyZAgAwMfHB9euXUNcXBwDkgh4DpKRMTMzg7+/P5KTk7VtarUaycnJCAoKErEy46TRaBAdHY0ff/wR+/fvR6tWrcQuyaj16dMHv/32G06dOqV9BAQEYNiwYTh16hTDkZ5169at3GUrfv/9d7Rs2VKkioxbYWEhpFLdP8symQxqtVqkip5v3INkhJRKJUaNGoWAgAAEBgYiISEBjx49QmRkpNilGZ3x48djy5Yt2LVrF2xsbJCTkwMAaNq0KSwtLUWuzvjY2NiUO7+rSZMmcHBw4HlfDWDy5Mno2rUrPvvsM7z99ttIT0/H2rVrsXbtWrFLM0qDBg3C/Pnz8cILL6B9+/Y4efIk4uPj8X//939il/Zc4tf8jdSKFSuwaNEi5OTkwM/PD1988QUUCoXYZRkdiURSYfvGjRsxevRowxbznOrVqxe/5t+Adu/ejZiYGFy+fBmtWrWCUqlEVFSU2GUZpQcPHmDGjBn48ccfcfv2bbi6umLo0KGYOXMmzMzMxC7vucOARERERCTAc5CIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIgA3LlzB3K5HJ999pm27ejRozAzM0NycrKIlRGRGHgvNiKi/2/Pnj0ICwvD0aNH0bZtW/j5+eGNN95AfHy82KURkYExIBER/c348eOxb98+BAQE4LfffsPx48dhbm4udllEZGAMSEREf/P48WN06NAB169fR0ZGBnx8fMQuiYhEwHOQiIj+5sqVK8jOzoZarcbVq1fFLoeIRMI9SERE/19JSQkCAwPh5+eHtm3bIiEhAb/99hucnJzELo2IDIwBiYjo/5syZQr++c9/4vTp07C2tkbPnj3RtGlT7N69W+zSiMjAeIiNiAhASkoKEhIS8O2338LW1hZSqRTffvstfv31V6xevVrs8ojIwLgHiYiIiEiAe5CIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgEGJCIiIiIBBiQiIiIiAQYkIiIiIgE/h84aSmRnVOOeAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = int(20)\n", + "p = 0.23\n", + "mu = n*p\n", + "\n", + "x = np.arange(0, 10)\n", + "\n", + "pmf_pois = np.array([poisson_pmf(k, mu) for k in x])\n", + "pmf_bin = np.array([binomial_pmf(k,n,p) for k in x])\n", + "\n", + "plt.bar(x, pmf_pois, label='poisson', alpha=0.5)\n", + "plt.bar(x, pmf_bin, label='binomial', alpha=0.5)\n", + "plt.xlabel('x')\n", + "plt.ylabel('P(X=x)')\n", + "plt.title('Poisson vs Binomial')\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0fbbdae1-01a7-4ad1-a099-31fc9436527c", + "metadata": {}, + "source": [ + "ii) $n=3.10^5$, $p=10^{-6}$
\n", + "$\\lambda=np=0.3$" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "0419d635-43dd-406c-ba05-72b2ad8ee449", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = int(3e5)\n", + "p = int(1e-6)\n", + "mu = 0.3\n", + "\n", + "x = np.arange(0, 10)\n", + "\n", + "pmf_pois = np.array([poisson_pmf(k, mu) for k in x])\n", + "pmf_bin = np.array([binomial_pmf(k,n,p) for k in x])\n", + "\n", + "plt.bar(x, pmf_pois, label='poisson', alpha=0.5)\n", + "plt.bar(x, pmf_bin, label='binomial', alpha=0.5)\n", + "plt.xlabel('x')\n", + "plt.ylabel('P(X=x)')\n", + "plt.title('Poisson vs Binomial')\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "32ea2406-6b1e-48b1-bc93-eca11119ba64", + "metadata": {}, + "source": [ + "**Question 2:**

\n", + "$X,Y\\to N(0,1)$\n", + "
$W=XY+X^2Y+XY^2$
\n", + "$Z=X^3Y+XY^3$
\n", + "$Cov(X,Y)=E(WZ)-E(W)E(Z)$
\n", + "$Cov(X,Y)=E(X^2Y^4+X^4Y^2+X^3Y^4+X^5Y^2+X^2Y^5+X^4Y^3)-E(XY+X^2Y+XY^2)E(XY^3+X^3Y)$
\n", + "$=E(X^2Y^4)+E(X^4Y^2)+E(X^3Y^4)+E(X^5Y^2)+E(X^2Y^5)+E(X^4Y^3)$
$-(E(XY)+E(X^2Y)+E(XY^2))(E(X^3Y)+E(XY^3)$

\n", + "since X,Y are just two standard normal distributions which are not related to each other therefore they are independent using this

\n", + "$Cov(X,Y)=E(X^2)E(Y^4)+E(X^4)E(Y^2)+E(X^3)E(Y^4)+E(X^5)E(Y^2)+E(X^2)E(Y^5)+E(X^4)E(Y^3)$
$-(E(X)E(Y)+E(X^2)E(Y)+E(X)E(Y^2))(E(X^3)E(Y)+E(X)E(Y^3)$

\n", + "on expansion we get both $E(WZ)$ and $E(W)E(Z)$ as equal\n", + "therefore $Cov(X,Y)=0$

" + ] + }, + { + "cell_type": "markdown", + "id": "41c4f2d8-3cff-4cdf-a623-6322fa52f194", + "metadata": {}, + "source": [ + "**Question 3:**

\n", + "$\\bar{X}=\\frac{X_1+X_2+X_3...+X_n}{n}$
\n", + "$E(\\bar{X})=\\mu$
\n", + "$Var(\\bar{X})=\\frac{\\sigma^2}{n}$
\n", + "using chebyshev's inequality
\n", + "$P(|\\bar{X}-\\mu|\\geq\\epsilon)\\leq\\frac{\\sigma^2}{n\\epsilon^2}$
\n", + "now since n is very large $n\\to\\infty$
\n", + "therefore, $P(|\\bar{X}-\\mu|\\geq\\epsilon)\\leq0$" + ] + }, + { + "cell_type": "markdown", + "id": "0e635d7c-6a9a-4576-a923-751d4adf45ec", + "metadata": {}, + "source": [ + "
**Question 4:**\n", + "\n", + "| $x$ | $P(X = x)$ |\n", + "|-----|------------|\n", + "| 1 | $\\frac{2}{24}$ |\n", + "| 2 | $\\frac{3}{24}$ |\n", + "| 3 | $\\frac{1}{24}$ |\n", + "| 4 | $\\frac{1}{24}$ |\n", + "| 5 | $\\frac{5}{24}$ |\n", + "| 6 | $\\frac{1}{24}$ |\n", + "| 7 | $\\frac{2}{24}$ |\n", + "| 8 | $\\frac{9}{24}$ |" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "d1daee78-afeb-45ac-ba9c-09e6988689d6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "X = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n", + "P = np.array([2/24, 3/24, 1/24, 1/24, 5/24, 1/24, 2/24, 9/24])\n", + "\n", + "means = []\n", + "for _ in range(10000):\n", + " samples = np.random.choice(X, size=10000, p=P)\n", + " mean = np.mean(samples)\n", + " means.append(mean)\n", + "\n", + "# Plot histogram\n", + "plt.hist(means, bins=30, edgecolor='black')\n", + "plt.title('Histogram of Means')\n", + "plt.xlabel('Mean')\n", + "plt.ylabel('Frequency')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "98af8aba-893d-4822-8d40-0a47bba58c5b", + "metadata": {}, + "source": [ + "
$\\mu=5.5$
\n", + "$\\sigma=2.483$
\n", + "$S=0.02483$
\n", + "By CLT $\\bar{X}\\to N(5.5,0.02483)$" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "58c84211-beb3-402b-aeb1-e06325a8bdf9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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OTg6ys7Px77//YunSpWjfvv0DFXU6D9z2Jkp3UVy5ckVYWlqKF154QXf/vV1s0dHRAoB48sknSz3PrFmzBACxc+dO3bLAwEABQPz999+l1t21a5cAIJo0aSIKCwt1y8eMGSNkMpno169fqfXbt29fpkuuvC7UPn36iODg4FLLqtv1qfXFF18IAOL333/XLQMg3nnnHd1tJyen+3ahVdS9qH1NgoODy+Smva9ks3nXrl0FAPH555/rlhUUFIjw8HDh4eGhe121+/feLr/ynrOi2MrrCtFu5/bt27plJ0+eFHK5XEyYMEG3TNs19MQTT5R6zmHDhglXV9cy2ypJrVYLR0dH8eqrrwohirvOXV1dxciRI4WFhYXIysoSQgixYMECIZfLxZ07d3SPvXff3K/r08rKSly+fLlULgDEokWLKo1R+9p8+umn4syZMwKAiIqKEkII8c033wh7e3uRk5NTpisvKytLODs7i6eeeqrU8yUlJQknJ6dSy8t7r69evVoAEHv27NEtq85rXfLx9/t7kO7xtWvXikmTJonly5eLjRs3irfeekvY2toKNzc3ER8ff9/Hv/766+K1114Ta9euFatXrxYTJ04UAETHjh2FSqW67+Pvfc0KCwtFkyZNxCOPPFJq+YPu+6FDhwpra2sRFxenW3bu3DlhYWFx365PIYSYM2eOACDs7OxEv379xAcffCCOHTtWZr3Kuj7Lex989NFHQiaTlYpL+1q9++67pdaNiIgQLVu21N3etGmTACA++eQT3bKioiLRuXPnMjFU9T04ZsyYUuumpKQIKysrMWDAgFLdS2+88YYAUK2uT60XX3xRABAnT54UQgjxyy+/CLlcrvs8an377bcCgNi3b58QQoiLFy+W+1mfPn26sLe3L5X7vceV8l6XAwcOCADi559/1i2rrOvz3u+ohQsXCgBixYoVumWFhYWiffv2wt7eXmRmZgoh/jv2uLq6lupa/P333wUA8ccff1T0UpV6/IP83a/L9tlnnxUWFhbl3ufu7i5Gjx5d6ePDwsLKfDaFEOLs2bMCgPj2228rfGxBQYFo3LixCAoKKnNs+PPPP4WlpaU4e/asEKLiUyqSk5NFjx49SuXs5uYm9u/fX+42P/roo1Lr9ujR44GOayU99PAcwcHBGD9+PL7//nvcvHmz3HW2bt0KAGVO2tSehH9vE2dQUBD69OlT7nNNmDChVJXetm1bCCHKtAa1bdsW169fR1FRkW5Zyco1IyMDqamp6Nq1K65evYqMjIz7pVpl2l/xWVlZFa7j7OyMQ4cOITEx8aG3M3HixAeuyi0tLfH000/rbltZWeHpp59GSkoKjh079tAx3M/NmzcRHR2NSZMmlWodaNasGXr16qV7j5Q0bdq0Urc7d+6M27dvV9qtJZfL0aFDB+zZswdAcbP27du38frrr0MIgQMHDgAobmVr0qRJtS4S6NmzJ0JCQkrl4ujoiKtXrz7wc4SFhaFZs2ZYvXo1gOJfukOGDIGtrW2ZdSMjI5Geno4xY8YgNTVV92dhYYG2bdti165dunVLvh/y8/ORmpqKdu3aAYCuW72kh3mtgeLPY2Rk5H3/Vq5ced/XYtSoUVi6dCkmTJiAoUOH4r333sO2bdtw+/btMt1T5fnoo4/w8ccfY9SoURg9ejSWLVuGDz74APv27Su3C/NeJV+zO3fuICMjA507dy739brfvler1di2bRuGDh2KgIAA3XqhoaEVHtvuNW/ePKxatQoRERHYtm0b3nzzTbRs2RItWrQot7vmfjnl5OQgNTUVHTp0gBBC16JRUnnvg5Lv561bt8LS0lLXwgYUt5Y+//zzlW77Yd6D27dvR2FhIZ5//vlSrW9Vuajqfu49Rq9fvx6hoaFo1KhRqc/YI488AgC6z1iDBg0QHh6OtWvX6p5LrVbj119/xaBBgyo9Hpe8T6VS4fbt26hXrx6cnZ3LfV0exNatW+Hl5YUxY8bolikUCrzwwgu6FpySHnvssVIt3NqW2Psdu7y8vB7o8x4ZGYnmzZtX+lyVXexmbW1dpnu+vMcrlcpyH6u9vyLPPfcczp07h6+//rpU12ZhYSFeeuklTJs2DY0bN650+7a2tmjYsCEmTpyI9evX46effoK3tzeGDx+Oy5cvl1l/zJgxiIyMxKpVqzB27Nj7xlieh+r61Hrrrbfwyy+/4OOPP8aXX35Z5v64uDjI5XLUq1ev1HIvLy84OzsjLi6u1PJ7r/gqqeRBD/jviq57mzidnJyg0WiQkZGh64rYt28f3nnnHRw4cKBMd01GRoberw7Lzs4GADg4OFS4zieffIKJEyfC398fLVu2RP/+/TFhwgQEBwc/8HYqe73u5ePjU+YqlgYNGgAoPn9BeyDVN+0+LtmNrRUaGopt27YhJyenVGz37mvtgeXOnTtlmrtL6ty5s65rNSoqCt7e3mjRogWaN2+OqKgo9OrVC3v37sWoUaOqldO98WljvHPnTpWeZ+zYsfj888/x0ksvYf/+/XjjjTfKXS8mJgYAdF8a9yr5mqSlpWHevHlYs2YNUlJSSq1X3o+Sh32tg4ODq/RerapOnTqhbdu22L59+0M9/qWXXsLbb7+N7du3V9odBQB//vkn3n//fURHR5c6H6m8Mc/ut+9v3bqFvLy8crtsGzZsWO4Pk/KMGTMGY8aMQWZmJg4dOoRly5Zh1apVGDRoEM6cOXPfK4Pj4+MxZ84cbN68ucz78t73gbW1damu/XtzAoo/x97e3mW6ksv7XFf1PXjvcUx7zLj3NXR3d3/gbvT7ufcYHRMTg/Pnz5d5HbRK5vHYY4/hjTfeQEJCAnx9fbF7926kpKTgscceq3SbeXl5+Oijj7B06VIkJCSUOof5YRsM4uLiUL9+fcjlpdtctF2l937HVvZ5r4y1tTV69uz5UDHey8bGpsIu7Pz8/Ps2PtjY2JQ5D137WO395fn000+xZMkSvPfee+jfv3+p+7744gukpqZi3rx5941/5MiRulOotIYMGYL69evjzTffLFXEA8UjIQQGBgIo/lxPnToVPXv2xMWLFx+8oeWB1qpAcHAwHn/8cXz//fd4/fXXK1zvQQd5rCxoCwuLKi3XfgiuXLmCHj16oFGjRliwYAH8/f1hZWWFrVu34osvvoBGo3mg2KrizJkzAFCmQC1p1KhR6Ny5MzZu3Ih//vkHn376KebPn48NGzagX79+D7SdKvVxP4CK9tPDntz9sO63TyvSqVMnqFQqHDhwAFFRUbpfi507d0ZUVBQuXLiAW7du6ZbXdnz3GjNmDGbPno2nnnoKrq6u6N27d7nrad+jv/zyS6nzYrRK/jIcNWoU9u/fj1deeQXh4eGwt7eHRqNB3759y32vP2wu2dnZui+7ylhYWFT45Xc//v7+uHjx4kM9Vnuy9v3Oq4mKisLgwYPRpUsX/O9//4O3tzcUCgWWLl1a5mIPQH/7/kE5OjqiV69e6NWrFxQKBZYvX45Dhw6ha9euFT5GrVajV69eSEtLw2uvvYZGjRrBzs4OCQkJmDRpUpn3QUU5Payqvgf1fRx7EGfOnIGFhYWuSNRoNGjatGmZYZW0SjYIPPbYY5g9ezbWr1+PGTNmYN26dXByctINm1KR559/HkuXLsWMGTPQvn17ODk5QSaTYfTo0TXyPVSeh33/qtVq3Lp164G24eLiUun50t7e3lCr1UhJSdFdHAMUt2rdvn270nPetY8vbxxXbc9eeY9ftmwZXnvtNUybNq3MsEgZGRl4//33MX36dGRmZup6E7KzsyGEQGxsLGxtbeHh4YGrV6/i77//xvfff18m506dOmHfvn2Vxg4AI0aMwJIlS7Bnz54HbmWvVqEGFLeqrVixotyTjwMDA6HRaBATE1PqZMjk5GSkp6frqsya9Mcff6CgoACbN28u9WuiZHeRPmVnZ2Pjxo3w9/ev8ARQLW9vb0yfPh3Tp09HSkoKWrRogQ8++EBXqOlzFPPExMQyLVeXLl0CAN2J6NpfV/deyXXvr7KqxKbdx+V94V64cAFubm4VjldTVW3atIGVlRWioqIQFRWlu3qzS5cuWLJkCXbs2KG7XZnaGj0+ICAAHTt2xO7du/HMM89UeJWRtqvNw8Oj0l+1d+7cwY4dOzBv3rxSF9NoW+T06bPPPnugX5+BgYEPPXDn1atXH7rIy8rKQmpq6n0f/9tvv8Ha2hrbtm0r1Z2ydOnSh9quu7s7bGxsyn3NH7bo1GrVqhWWL1+u+0Kq6H16+vRpXLp0CcuXL8eECRN0y+8dELQqAgMDsWPHDmRnZ5dqVbs3J328B7XHjJiYmFKttrdu3apyq3V54uPj8e+//6J9+/a6FrWQkBCcPHkSPXr0uO/nPygoCG3atMHatWvx3HPPYcOGDRg6dGi53XEl/frrr5g4cSI+//xz3bL8/Pwyx9uqHH8CAwNx6tQpaDSaUq1qFy5c0N2vD9evX3/gHpxdu3ZVOnuCdsy/o0ePlmrZOnr0KDQazX3HBAwPDy91IYiWdrD5ex//+++/48knn8Tw4cPxzTfflHm+O3fuIDs7G5988gk++eSTMvcHBQVhyJAh2LRpE5KTkwGU33ihUqlKnXJVEW23Z1VaUas9hVRISAgef/xxfPfdd2VGEdfuhHtHsNf+arn3iqqaoP0FcW8z88MeiCuTl5eH8ePHIy0tDW+++WalLVT37iQPDw/4+PiUatK1s7PT2zl0RUVFpYYIKCwsxHfffQd3d3e0bNkSwH8FgfY8L22s9/56qEps3t7eCA8Px/Lly0sdkM6cOYN//vmnTBN0dVhbW6N169ZYvXo14uPjS7Wo5eXl4auvvkJISAi8vb0rfR5t4ajvmQnK8/777+Odd94p91wfrT59+sDR0REffvghVCpVmfu1v3TLe68DZT9/+qDPc9TK+6W+detWHDt2rEwrxZUrV3DlyhXd7fz8/HLPBX3vvfcghLhvK4eFhQVkMlmpA29sbKzuKr+qsrCwQJ8+fbBp0ybEx8frlp8/fx7btm277+Nzc3N151Pe66+//gLwX3djRe/T8t4HQohyT095UP3790dRUVGpYY3UanWZQc/18R7s2bMnFAoFFi1aVOp59PE+TktLw5gxY6BWq/Hmm2/qlo8aNQoJCQlYsmRJmcdor9or6bHHHsPBgwfx008/ITU19b7dnkDxa3Pv67Jo0aIyX/pVOf70798fSUlJpbrbioqKsGjRItjb21fa8loV+jxH7ZFHHoGLi0uZIbIWL14MW1vbUnVBamoqLly4UOqUpREjRpT5XiooKMDSpUvRtm3bUq2fe/bswejRo9GlSxesXLmyTBcxUPzdu3HjxjJ/3bt3h7W1NTZu3IjZs2cDKO4lk8vlWLt2bal9eePGDURFRSEiIkK3rKIWyB9//BEymQwtWrSo9HUqqdotakDxcA2//PILLl68WGo4iubNm2PixIn4/vvvkZ6ejq5du+Lw4cNYvnw5hg4dWu54NPrWu3dvWFlZYdCgQXj66aeRnZ2NJUuWwMPDo8KLIB5EQkICVqxYAaC4Fe3cuXNYv349kpKS8PLLL5c6cf9eWVlZ8PPzw4gRI9C8eXPY29tj+/btOHLkSKlfWy1btsTatWsxc+ZMtG7dGvb29hg0aNBDxevj44P58+cjNjYWDRo0wNq1axEdHY3vv/9ed5FGWFgY2rVrh9mzZyMtLQ0uLi5Ys2ZNub8SqhLbp59+in79+qF9+/aYMmWKbngOJycnvc+F17lzZ3z88cdwcnJC06ZNARR/EBs2bIiLFy8+0DyB2sL1zTffxOjRo6FQKDBo0CC9tfyV1LVr1/seTB0dHbF48WKMHz8eLVq0wOjRo+Hu7o74+Hhs2bIFHTt2xNdffw1HR0d06dIFn3zyCVQqFXx9ffHPP//g2rVreo9bn+eodejQAREREWjVqhWcnJxw/Phx/PTTT/D39y9z3l6PHj0AQNdKl5SUhIiICIwZM0Y3ZdS2bduwdetW9O3bF0OGDKl02wMGDMCCBQvQt29fjB07FikpKfjmm29Qr149nDp16qHymTdvHv7++2907twZ06dP131xhoWF3fc5c3Nz0aFDB7Rr1w59+/aFv78/0tPTsWnTJkRFRWHo0KG6L4OQkBA4Ozvj22+/hYODA+zs7NC2bVs0atQIISEhmDVrFhISEuDo6IjffvutWq1RgwYNQseOHfH6668jNjYWjRs3xoYNG8r8WNPHe1A7jttHH32EgQMHon///jhx4gT++uuvcodUqMilS5ewYsUKCCGQmZmJkydPYv369cjOztbtc63x48dj3bp1mDZtGnbt2oWOHTtCrVbjwoULWLdunW58T61Ro0Zh1qxZmDVrFlxcXB7o/K2BAwfil19+gZOTExo3bowDBw5g+/btZYb0CQ8Ph4WFBebPn4+MjAwolUrdOKD3mjp1Kr777jtMmjQJx44dQ926dfHrr79i3759WLhwYaXnSVeFvs9Re++99/Dss89i5MiR6NOnD6KiorBixQp88MEHpS46+/rrrzFv3rxSrXRt27bFyJEjMXv2bKSkpKBevXpYvnw5YmNj8eOPP+oeGxcXh8GDB0Mmk2HEiBFlhqVp1qwZmjVrBltbWwwdOrRMnJs2bcLhw4dL3efu7o4nnngCP/zwA3r06IHhw4cjKysL//vf/5CXl6cr6ADoLmjq27cvAgICkJaWht9++w1HjhzB888/X+mpUWVU5RLRykYQ117mfe8I+CqVSsybN08EBQUJhUIh/P39xezZs0V+fn6p9Soa8kI7NMT69esfKBbtJd+3bt3SLdu8ebNo1qyZsLa2FnXr1hXz588XP/30U5khGKoyPAfuXmork8mEo6OjCAsLE0899ZQ4dOhQuY9BiUu1CwoKxCuvvCKaN28uHBwchJ2dnWjevHmZ2Qyys7PF2LFjhbOzc6mhDip6TUred+/wHGFhYeLo0aOiffv2wtraWgQGBoqvv/66zOOvXLkievbsKZRKpfD09BRvvPGGiIyMLPOcFcVW0Ujl27dvFx07dhQ2NjbC0dFRDBo0SJw7d67UOuXtOyEqHjakPFu2bBEAygzb8uSTTwoA4scffyzzmJL7Ruu9994Tvr6+Qi6Xl9o2Krjs/0FGTC85PEdlKrosfNeuXaJPnz7CyclJWFtbi5CQEDFp0iRx9OhR3To3btwQw4YNE87OzsLJyUmMHDlSJCYmlslRH6+1vrz55psiPDxcODk5CYVCIQICAsQzzzwjkpKSyqwbGBhYasiPO3fuiMcff1zUq1dP2NraCqVSKcLCwsSHH35Yajifyvz444+ifv36QqlUikaNGomlS5eWO4tAVfb9v//+K1q2bCmsrKxEcHCw+Pbbbx94ZoIlS5aIoUOHisDAQKFUKoWtra2IiIgQn376qSgoKCi1/u+//y4aN24sLC0tS33uzp07J3r27Cns7e2Fm5ubeOqpp3RDiZT8bFb0Xisv1tu3b4vx48cLR0dH4eTkJMaPHy9OnDhR5jmr+x4Uoni4nXnz5glvb29hY2MjunXrJs6cOVOlmQm0f3K5XDg7O4uIiAjx4osv6oZfuFdhYaGYP3++CAsLE0qlUtSpU0e0bNlSzJs3T2RkZJRZv2PHjgLlDD9VMoaS+d65c0dMnjxZuLm5CXt7e9GnTx9x4cKFcnNasmSJCA4O1g3poj32lvcdlZycrHteKysr0bRp0zLH38qOPeUd/2rD999/Lxo2bCisrKxESEiI+OKLL0oNxyLEf++Re4f8yMvLE7NmzRJeXl5CqVSK1q1bVzi0V0V/98u5os+GSqUSixYtEuHh4cLe3l7Y29uL7t27lxpuTAgh/vnnHzFw4EDh4+MjFAqFcHBwEB07dhRLly4tk+f9yISoobNgiYiIiKhaqn2OGhERERHVDBZqRERERAaKhRoRERGRgWKhRkRERGSgWKgRERERGSgWakREREQGSi8D3hoTjUaDxMREODg41NpUQURERFQ9QghkZWXBx8en3FkGTJXZFWqJiYmlppggIiIi43H9+nX4+flJHUatMbtCTTulxvXr10tN6KpSqfDPP/+gd+/euimVTJ255Wxu+QLml7O55QuYX87mli/AnLU5Z2Zmwt/fX29TYxkLsyvUtN2djo6OZQo1W1tbODo6mtUHwZxyNrd8AfPL2dzyBcwvZ3PLF2DO9+ZsbqctmU8nLxEREZGRYaFGREREZKBYqBEREREZKBZqRERERAaKhRoRERGRgWKhRkRERGSgWKgRERERGSgWakREREQGioUaERERkYFioUZERERkoFioERERERkogyrU9uzZg0GDBsHHxwcymQybNm0qs8758+cxePBgODk5wc7ODq1bt0Z8fHztB0tERERUwwyqUMvJyUHz5s3xzTfflHv/lStX0KlTJzRq1Ai7d+/GqVOn8Pbbb8Pa2rqWIyUiQ6PWCKRmFyCjELiTWwghhNQhERFVm6XUAZTUr18/9OvXr8L733zzTfTv3x+ffPKJbllISEhthEZEBuZ6Wi4izyXj8LU0nE7IwM2MPGgEAFhizrHdsLKUI8DFFhH+zmgX7IqeoZ5wslVIHTYRUZUYVKFWGY1Ggy1btuDVV19Fnz59cOLECQQFBWH27NkYOnRohY8rKChAQUGB7nZmZiYAQKVSQaVS6ZZr/19ymakzt5zNLV/A9HIuUmsQeT4Fyw/E41h8epn7ZQBkENBAhsIiDS6nZONySjbWH7sBhYUM3Ru6Y3KHQLQMcIZMJqv1+GuCqe3j+zG3fAHmfO8ycyMTBto/IJPJsHHjRl0RlpSUBG9vb9ja2uL9999H9+7d8ffff+ONN97Arl270LVr13KfZ+7cuZg3b16Z5atWrYKtrW1NpkBEeiIEcDJNhs1xctwuKC6wZBAIcRRo7CwQaC/gYQPYKwC5DFBrgPRCIClPhqtZMpxJkyEp77/CrJ6jBsPqauBnJ1VGRFRVubm5GDt2LDIyMuDo6Ch1OLXGaAq1xMRE+Pr6YsyYMVi1apVuvcGDB8POzg6rV68u93nKa1Hz9/dHampqqR2tUqkQGRmJXr16QaEwj+4Rc8vZ3PIFTCPna6k5ePP3czgSewcA4GKnwJjW/hjT2g+ejqXPT60s3wtJWfjlYDw2nbyJwiINZDJgZAtfvN63IRysjaZzoQxT2MdVYW75AsxZm3NmZibc3NzMrlAzmqOTm5sbLC0t0bhx41LLQ0NDsXfv3gofp1QqoVQqyyxXKBTlvuErWm7KzC1nc8sXMM6chRBYeSgeH2w5jzyVGtYKOaZ2CcG0rsGwtar80FVevk39XfCJvwte7NUQ8/+6gM0nE7HuWAL2XUnDF4+Fo02QS02mU+OMcR9Xh7nlCzBnc8tdy6Cu+qyMlZUVWrdujYsXL5ZafunSJQQGBkoUFRHVhLxCNZ5ffQJvbTqDPJUaHUJcsX1mV8zs1eC+Rdr9+Drb4KsxEVg7tR386tggIT0Pj31/AEv2XOWVokRkcAyqRS07OxuXL1/W3b527Rqio6Ph4uKCgIAAvPLKK3jsscfQpUsX3Tlqf/zxB3bv3i1d0ESkV0kZ+Zj6y1GcupEBS7kMr/drhCc6BkEu1+/J/22DXfHXi50xd/M5/Hb8Bj7Yeh4Xk7PwwbAmUFpa6HVbREQPy6AKtaNHj6J79+662zNnzgQATJw4EcuWLcOwYcPw7bff4qOPPsILL7yAhg0b4rfffkOnTp2kCpmI9Cg2NQfjfjiEhPQ81LFVYPHjLdEu2LXGtudgrcBnI5uhia8j3vvzHH49dgPJmfn4fnwr2FixWCMi6RlUodatW7f7dj088cQTeOKJJ2opIiKqLZeSszDuh0O4lVWAYDc7LH+iDfxdav7KbJlMhskdgxDsbo9nVhxDVEwqJv50GD9OagUHa/M8J4aIDIfRnKNGRKbr6q1sjPn+IG5lFaCRlwPWPt2+Voq0kro2cMcvU9rCwdoSh2PTMOGnw8gtLKrVGIiI7sVCjYgklZSRj/E/HsbtnEI08XXEmqnt4O5Q9krt2tAysA5WP9UOTjYKnIhPx9O/HENhkUaSWIiIABZqRCSh9NxCTPip+Jy0YDc7LJ/cBs62VpLG1MTXCUsnt4aNwgJRMamYuS4aGg2vBiUiabBQIyJJqNQaTP3lGC4lZ8PTUYmfp7SBq700LWn3ahFQB9+NbwmFhQx/nrqJhTtipA6JiMwUCzUiksS7f5zD4WtpcFBa4ucn2sKvjmFN6dalgTs+HNYUAPDVjhhsOXVT4oiIyByxUCOiWrfmcDx+ORgHmQxYODocDb0cpA6pXCNb+ePJTkEAgJfXR+NMQobEERGRuWGhRkS16nj8Hbz9+xkAwMu9GqBHqKfEEVVudv9QdG3gjnyVBtNWHENGnkrqkIjIjLBQI6Jak5mvwgurT0ClFujXxAvPdq8ndUj3ZSGX4asxEfB3scGNO3mYveEUp5oiolrDQo2IaoUQAm9sOI0bd/Lg72KD+SOaQSbT77RQNcXJRoFFY1rAUi7D1tNJWHkoXuqQiMhMsFAjolqx/tgN/HnqJizlMnw1OgKORjbqf7i/M17r2wgA8O6f53AhKVPiiIjIHLBQI6IaF3c7B3M3nwUAvNSrASIC6kgc0cOZ0ikI3Ru6o7BIg5fXnYRKzcFwiahmsVAjohql0Qi8/ttp5Baq0TbIBdO6hkgd0kOTy2WYP6IZnG0VOJuYif/tuiJ1SERk4lioEVGNWn0kHgeu3oaNwgKfjGgGC7lxnJdWEQ8Ha7w7pAkAYNHOGJxN5JAdRFRzWKgRUY1JTM/DR1svAABe6dMQga52EkekH4OaeaNvmBeKNAKz1p9iFygR1RgWakRUI4QQeGPjaWQXFKFlYB1M7FBX6pD0RiaT4f1hTeBiZ4XzNzPx495rUodERCaKhRoR1YjNJxOx++ItWFnKMf9R4+/yvJebvRJv9A8FAHy5PQYJ6XkSR0REpoiFGhHpXXZBET7ceh4A8Hz3eqjnYS9xRDXj0Ra+aFPXBXkqNebdvaqViEifWKgRkd59tSMGyZkFqOtqi6ldg6UOp8Zou0At5TL8cy4ZO84nSx0SEZkYFmpEpFcxyVn46e45W+8MCoPS0kLiiGpWA08HTOlcPHH7O5vPIq9QLXFERGRKWKgRkd4IIfDO5rMo0gj0DPVE90YeUodUK154pD58nKxx404evt9zVepwiMiEsFAjIr3560wS9l+5DStLOd4Z1FjqcGqNndISs+9eWPDtv1eQnJkvcUREZCpYqBGRXhQWafDxX8Vjpk3rGgJ/F1uJI6pdA5t5IyLAGXkqNT7/56LU4RCRiWChRkR6seJgHOLTcuHuoMTTXUz3AoKKyGQyvD2wuBVx/bEbnLGAiPSChRoRVVtGngpf7YwBALzUswHslJYSRySNFgF1MKi5D4QAPthyHkIIqUMiIiPHQo2Iqm3x7itIz1Whnoc9RrXykzocSb3apyGsLOXYf+U2dl5IkTocIjJyLNSIqFoS0vPw077i4The79sIlhbmfVjxd7HF5I51AQCfbrsIjYatakT08Mz7iEpE1fZF5CUUFmnQNsgFPULNYziO+3mmawgcrC1xISkLf5xKlDocIjJiLNSI6KFdvZWNDcdvAABe79cIMplpzef5sJxtrXQXVHwReQkqtUbiiIjIWLFQI6KH9uWOGGgE0KORByIC6kgdjkGZ3DEIrnZWiL2di9+O3ZA6HCIyUizUiOihxCRnYfPJ4m69l3o1kDgaw2OntMT07vUAFBe0+SpOLUVEVcdCjYgeysLtMRAC6BPmiSa+TlKHY5DGtQ2At5M1bmbkY+WheKnDISIjZHCF2p49ezBo0CD4+PhAJpNh06ZNFa47bdo0yGQyLFy4sNbiIyLg/M1MbDl9EwAwoydb0ypirbDACz3qAyieWoqtakRUVQZXqOXk5KB58+b45ptvKl1v48aNOHjwIHx8fGopMiLSWrj9EgBgQDNvhHo7ShyNYXu0hR98nW1wK6sA645elzocIjIyBleo9evXD++//z6GDRtW4ToJCQl4/vnnsXLlSigUilqMjojOJGRg29lkyGTAjLutRVQxK0s5pnUtvgL0291XUFjEK0CJ6MEZXKF2PxqNBuPHj8crr7yCsLAwqcMhMjuLd18BAAxs5oP6ng4SR2McRrbyh4eDEokZ+brhTIiIHoTRTcg3f/58WFpa4oUXXnig9QsKClBQUKC7nZmZCQBQqVRQqVS65dr/l1xm6swtZ3PLF9B/zldv5WDrmeJz06Z2CjS419JQ97EFgCc71cWHf13EN7suY0gzT73N4GCoOdcUc8sXYM73LjM3MmHAswbLZDJs3LgRQ4cOBQAcO3YMAwYMwPHjx3XnptWtWxczZszAjBkzyn2OuXPnYt68eWWWr1q1Cra2tjUVOpFJWnVZjkO35GhSR4OnGrELryoK1cC84xbILpJhXD012rgb7KGXyCDl5uZi7NixyMjIgKOj+Zwba1SF2sKFCzFz5kzI5f/9ElWr1ZDL5fD390dsbGyZ5yivRc3f3x+pqamldrRKpUJkZCR69eplNue9mVvO5pYvoN+cE9Pz0OOLvSjSCKyb2gYR/s76CVKPDH0ff7fnGj6LjEGwmy22Pt8RFvLqz+Rg6Dnrm7nlCzBnbc6ZmZlwc3Mzu0LNqLo+x48fj549e5Za1qdPH4wfPx6TJ08u9zFKpRJKpbLMcoVCUe4bvqLlpszccja3fAH95Lz0wCUUaQTaB7uiTbC7niKrGYa6jyd1CsaSvbG4mpqLnZduo39Tb709t6HmXFPMLV+AOZtb7loGV6hlZ2fj8uXLutvXrl1DdHQ0XFxcEBAQAFdX11LrKxQKeHl5oWHDhrUdKpHZuJ1dgDVHigdsnd49ROJojJe90hIT2wfiq52X8d2eq+jXxIvzoxJRpQzuqs+jR48iIiICERERAICZM2ciIiICc+bMkTgyIvO1dF8s8lUaNPNzQqd6blKHY9QmdKgLpaUcJ6+n4/C1NKnDISIDZ3Atat26dUNVTpsr77w0ItKfnIIi/HwgFgAwvVsIW4Cqyc1eiUdb+mHVoXh8v+cq2ga73v9BRGS2DK5FjYgMy/qj15GZX4QgNzv0buwldTgm4clOQZDJgB0XUhCTnCV1OERkwFioEVGF1BqBn/bFAgCe6BQEuR6uUiQg2N0evUI9AQBLoq5KHA0RGTIWakRUochzSYhPy4WzrQIjWvhJHY5JefrutFKbTiQiJTNf4miIyFCxUCOiCv0QdQ0A8HjbQNhYWUgcjWlpGeiCloF1UKjWYNn+WKnDISIDxUKNiMp1Iv4OjsbdgcJChgntA6UOxyRN7VLcqrbiYByyC4okjoaIDBELNSIq1w97i1vTBjf3hYejtcTRmKZeoZ4IdrNDZn4R1h+9LnU4RGSAWKgRURnX03Lx1+niydef7BwkcTSmSy6XYXLHugCAnw/EQaMx2Bn9iEgiLNSIqIxl+2OhEUCnem4I9TafOfWkMLyFHxyUlriWmoN/Y25JHQ4RGRgWakRUSnZBEdYeKe6Gm8LWtBpnp7TEqNb+AIpngCAiKomFGhGVsvH4DWQXFCHY3Q5d6xv25OumYmL7upDJgD2XbuFySrbU4RCRAWGhRkQ6QggsPxAHAJjQLpAD3NaSAFdb9GhUPACudrouIiKAhRoRlXDgym1cTsmGnZUFHm3JAW5rk/aigl+P3UBmvkraYIjIYLBQIyKd5Xdbc4a38IODtULaYMxMhxBX1PewR26hGuuP3pA6HCIyECzUiAgAkJCeh8hzyQDAAW4lIJPJMOluq9ry/bFQc6gOIgILNSK6a+XBOGjE3ZYdTwepwzFLwyJ84WSjQHxaLnZdSJE6HCIyACzUiAj5KjXW3B2SY2KHutIGY8ZsrSwxqlXxuYErDsVJHA0RGQIWakSELaduIi2nEL7ONujRyEPqcMza2LbF3c7/XrqF62m5EkdDRFJjoUZEuiEhxrULgKUFDwtSCnKzQ+f6bhACWHkoXupwiEhiPCITmbno6+k4eSMDVpZyPNbKX+pwCMC4u61q645eR0GRWuJoiEhKLNSIzNyKg8XnQg1s5g1Xe6XE0RAA9Az1gJejNdJyCvH3mSSpwyEiCbFQIzJjGXkq/HkqEcB/rTgkPUsLOUa3KW7dXHmQ3Z9E5oyFGpEZ23QiAfkqDRp5OaBFgLPU4VAJo1sHwEIuw+HYNFxMypI6HCKSCAs1IjMlhMCquyerj2kTAJmM83oaEi8na/QKLZ7/cyWH6iAyWyzUiMzU8fh0XEzOgrVCjqERvlKHQ+UY1y4AALDheAJyCookjoaIpMBCjchMaVvTBjbzgZMN5/U0RB1D3FDX1RbZBUXYfDJR6nCISAIs1IjMUEbufxcRjG0bIHE0VBG5XKa7yEN7dS4RmRcWakRmaOOJGygoKr6IIMLfWepwqBIjWvrBylKOs4mZOJOQIXU4RFTLWKgRmRkhBFYdLu72HNuWFxEYujp2Vugb5gUAWH2YQ3UQmRsWakRm5nj8HVxKzoa1Qo4h4byIwBiMbl08ptrm6ETkFvKiAiJzwkKNyMys5EUERqddsCsCXGyRVVCErac5UwGROWGhRmRGMnJV2HLqJgBeRGBM5HIZHrvbqrb2CLs/icwJCzUiM7KBFxEYrREt/WAhl+FI7B1cTsmWOhwiqiUGV6jt2bMHgwYNgo+PD2QyGTZt2qS7T6VS4bXXXkPTpk1hZ2cHHx8fTJgwAYmJHF+I6H6EELqT0XkRgfHxdLRG94YeANiqRmRODK5Qy8nJQfPmzfHNN9+UuS83NxfHjx/H22+/jePHj2PDhg24ePEiBg8eLEGkRMbl5I0MXErOhtKSFxEYK+1FBb8dT0BhkUbiaIioNlhKHcC9+vXrh379+pV7n5OTEyIjI0st+/rrr9GmTRvEx8cjIIDn3BBVZN3R6wCAfk28eBGBkerW0B0eDkqkZBVg+/lk9G/qLXVIRFTDDK5Qq6qMjAzIZDI4OzuXe39BQQEKCgp0tzMzMwEUd6OqVCrdcu3/Sy4zdeaWs7nlC/yXa2ZuPjZHF58iMDzC22RfA3PYx49G+GDxnmtYfSgOvRq5mUXOJZlbvgBzvneZuZEJIYTUQVREJpNh48aNGDp0aLn35+fno2PHjmjUqBFWrlxZ7jpz587FvHnzyixftWoVbG1t9RkukcE6ckuGFZct4KIUeDtCDTlPTzNaqfnAeycsIYPAnBZquCiljoioduTm5mLs2LHIyMiAo6Oj1OHUGqNtUVOpVBg1ahSEEFi8eHGF682ePRszZ87U3c7MzIS/vz969+5dakerVCpERkaiV69eUCjMo1vI3HI2t3yB/3KOKXIFkI7HO9bDwO4hUodVY8xlH+/IOIr9V9Nw27EBHusSaBY5a5nLPi6JORfnrO0RMzdGWahpi7S4uDjs3Lmz0spaqVRCqSz7k1OhUJT7hq9ouSkzt5zNLd/UfOBQbDpkMmBU6wCzyN3U9/HotoHYfzUNv51IxHN3C29Tz/le5pYvwJzNLXctoyvUtEVaTEwMdu3aBVdXV6lDIjJoh1OKL+7uVM8NfnXY3W8Kejf2hLOtAjcz8rH3cqrU4RBRDTK44Tmys7MRHR2N6OhoAMC1a9cQHR2N+Ph4qFQqjBgxAkePHsXKlSuhVquRlJSEpKQkFBYWShs4kQFSawQO3So+IW1kK3+JoyF9sVZYYOjdIVY2nOA4kkSmzOAKtaNHjyIiIgIREREAgJkzZyIiIgJz5sxBQkICNm/ejBs3biA8PBze3t66v/3790scOZHh2X/1NtILZXC0tkTvxp5Sh0N6NKKlHwAg8nwKcjlPO5HJMriuz27duqGyC1EN+CJVIoPz27Hi1pbBzb1hrbCQOBrSpya+Tgj1dsT5m5k4lirDCKkDIqIaYXAtakSkH+m5hYi8kAIAGNGCMxGYIm2rmvY8RCIyPfx0E5mozScTUVikga+tQJiP+Yw5ZE6GhvvAUi5DfI4MMcmcqJ3IFLFQIzJR2imj2nlwTkhT5WqvRPeG7gCA304kSBwNEdUEFmpEJuhsYgbOJGRCYSFDSzee12nKhkf4AAB+P3kTRWoW5USmhoUakQlaf/QGAKBXqAfszHOMSLPRtYEb7C0FUrML8e+lW1KHQ0R6xkKNyMQUFKmxKbq4G4wXEZg+hYUcrdyLW01/PXZD4miISN9YqBGZmJ3nU5Ceq4KXozU6hHDmDnPQxr24y3P7+WTcyeHg30SmhIUakYn57Xhxa9rwFr6wkMskjoZqg68dEObjAJVa4PdoXlRAZEpYqBGZkNvZBdh9sXjstOHs9jQrwyOK9/evx9n9SWRKWKgRmZDNJxNRpBFo7ueEeh4OUodDtWhgUy8oLGQ4k5CJ8zczpQ6HiPSEhRqRCdmg6/b0kzgSqm0udlboGVo8nysvKiAyHSzUiEzEpeQsnE7IgKVchkHNfaQOhySgnVJq04kEqDimGpFJYKFGZCK0rWndG3nAxc5K4mhICl0buMPNXonbOYXYdXeeVyIybizUiEyAWiOw6e4UQo/yIgKzZWkh111Ewu5PItPAQo3IBOy/koqkzHw42yrQvZGH1OGQhB69e37izgspuJ1dIHE0RFRdLNSITIC223NQMx8oLS0kjoak1NDLAc38nFCkEfjjZKLU4RBRNbFQIzJy2QVF+PtMEgCOnUbFht0dU23DCQ5+S2TsWKgRGbm/zyQhT6VGsJsdwv2dpQ6HDMCg5j6wlMtw6kYGLqdkSR0OEVUDCzUiI7fh7kj0w1v4QibjlFEEuNkr0a2hO4D/usWJyDixUCMyYgnpeThw9TYAYGgEuz3pP9pBjzeeSIBGIySOhogeFgs1IiO26UQChADaB7vCr46t1OGQAXmkkQccrS1xMyMfB+8W80RkfFioERkpIQR+K9HtSVSStcICA+/OUPEbuz+JjBYLNSIjdfJGBq7eyoG1Qo5+Tb2lDocMkHbw47/O3ERuYZHE0RDRw2ChRmSktBcR9A3zgr3SUuJoyBC1CKiDQFdb5Baqse1sktThENFDYKFGZIQKizTYfHcwU+1J40T3kslk/42pxu5PIqPEQo3ICO26mIL0XBU8HZXoWM9N6nDIgA2PKC7k911ORVJGvsTREFFVsVAjMkLabs+hEb6wkHPsNKpYgKstWtetA40Afo9mqxqRsWGhRmRk7uQUYueFFAD/tZYQVUbbPf7b8RsQgmOqERkTFmpERuaPU4lQqQWa+DqioZeD1OGQEejf1BtWlnJcSs7G2cRMqcMhoipgoUZkZLRjYrE1jR6Uk40CvRp7AuBFBUTGhoUakRG5nJKNk9fTYSGXYXC4j9ThkBEZfvfqz80nE1Ck1kgcDRE9KIMr1Pbs2YNBgwbBx8cHMpkMmzZtKnW/EAJz5syBt7c3bGxs0LNnT8TExEgTLFEt23ii+CKCbg3c4WavlDgaMiZdGrjD1c4KqdmFiIpJlTocInpABleo5eTkoHnz5vjmm2/Kvf+TTz7BV199hW+//RaHDh2CnZ0d+vTpg/x8XnZOpk2jEdh4t9vq0Zbs9qSqUVjIda2w2qnHiMjwGdxw5v369UO/fv3KvU8IgYULF+Ktt97CkCFDAAA///wzPD09sWnTJowePbo2QyWqVQev3kZiRj4crS3xSCMPqcMhI/RoCz8s3ReLf84lIyNPBScbhdQhEdF9GFyhVplr164hKSkJPXv21C1zcnJC27ZtceDAgXILtYKCAhQUFOhuZ2YWX/GkUqmgUql0y7X/L7nM1Jlbzsae7/pj1wEA/Zt6wQIaqFT3P8/I2HOuKnPLF6hazg3cbVDfww4xKTn4M/oGRrUyvpZZ7mPzUF7O5pR/STJhwIPqyGQybNy4EUOHDgUA7N+/Hx07dkRiYiK8vf+bhHrUqFGQyWRYu3ZtmeeYO3cu5s2bV2b5qlWrYGtrW2OxE+lTgRp466gFCjUyzGhShCCOykEPaUeCDJvjLRDiIPBCE7XU4RA9sNzcXIwdOxYZGRlwdHSUOpxaY1Qtag9j9uzZmDlzpu52ZmYm/P390bt371I7WqVSITIyEr169YJCYR7dAeaWszHn+3t0IgoPn0GAiw2mj+oEmezBZiMw5pwfhrnlC1Q95xaZ+fjjsz24kiVD0/bd4F/HuH6wch+bb87aHjFzY1SFmpeXFwAgOTm5VItacnIywsPDy32MUqmEUln26jiFQlHuG76i5abM3HI2xnx/P5UEAHi0hT+srKyq/HhjzLk6zC1f4MFz9ndVoGOIG/ZeTsWfp1PwQo/6tRCd/nEfm4eSOZtb7loGd9VnZYKCguDl5YUdO3bolmVmZuLQoUNo3769hJER1ZykjHzsvVw8nMLwFr4SR0OmQPs+2sAppYgMnsG1qGVnZ+Py5cu629euXUN0dDRcXFwQEBCAGTNm4P3330f9+vURFBSEt99+Gz4+Prrz2IhMzcYTCRACaBPkAn8X4+qmIsPUJ8wLtlZnEHs7F8fj09EysI7UIRFRBQyuUDt69Ci6d++uu609v2zixIlYtmwZXn31VeTk5GDq1KlIT09Hp06d8Pfff8Pa2lqqkIlqjBACG+6OefUoW9NIT+yUlujbxAsbjidgw/EbLNSIDJjBdX1269YNQogyf8uWLQNQfCXou+++i6SkJOTn52P79u1o0KCBtEET1ZAzCZmIScmG0lKOfk297/8Aogf0aIvioTn+PHUTBUW8+pPIUBlcoUZE/9GOIN87zAuO1uZ5Ii3VjHbBrvB2skZGngo7z6dIHQ4RVYCFGpGBUqk12HwyEQAvIiD9s5DLMPTuRO2/3Z2ajIgMDws1IgP178VbSMsphLuDEp3ruUkdDpmg4XcLtd0XU3A7u+A+axORFFioERkobbfnkOY+sLTgR5X0r76nA5r5OaFII/DH3dZbIjIsPPoTGaD03ELsuHve0KMtjW8+RjIe2la1DSfY/UlkiFioERmgP0/dRKFag1BvR4R6m8+cdlT7BjX3gaVchlM3MhCTnCV1OER0DxZqRAaIY6dRbXG1V6J7Iw8AvKiAyBCxUCMyMNdSc3A8Ph0WchkGh/tIHQ6ZAe0Pgk0nEqDWcEopIkPCQo3IwGy825rWpb4bPBw44wbVvO6NPOBko0BSZj4OXLktdThEVAILNSIDotEI3Undw1vwIgKqHUpLCwxqXjzzhfZqYyIyDHor1K5evaqvpyIyW4dj03DjTh4clJbo1dhT6nDIjGinlPr7TBKyC4okjoaItPRWqNWrVw/du3fHihUrkJ+fr6+nJTIr2osIBjTzhrXCQuJoyJyE+zsj2M0OeSo1/j6TJHU4RHSX3gq148ePo1mzZpg5cya8vLzw9NNP4/Dhw/p6eiKTl1eoxtbTxV+Q7Pak2iaTyXRTlW1g9yeRwdBboRYeHo4vv/wSiYmJ+Omnn3Dz5k106tQJTZo0wYIFC3Dr1i19bYrIJP1zrrjLyd/FBq0C60gdDpkh7dyfB67eRkJ6nsTREBFQAxcTWFpaYvjw4Vi/fj3mz5+Py5cvY9asWfD398eECRNw8+ZNfW+SyCRsuDuG1fAIP8jlMomjIXPkV8cW7YNdIUTxUB1EJD29F2pHjx7F9OnT4e3tjQULFmDWrFm4cuUKIiMjkZiYiCFDhuh7k0RGLyUzH1Exxa3OwznILUlI+/777fgNCMEx1YikprdCbcGCBWjatCk6dOiAxMRE/Pzzz4iLi8P777+PoKAgdO7cGcuWLcPx48f1tUkik7EpOgEaAbQKrINAVzupwyEz1q+pN6wVcly9lYPo6+lSh0Nk9vRWqC1evBhjx45FXFwcNm3ahIEDB0IuL/30Hh4e+PHHH/W1SSKTIITAb8c4dhoZBnulJfqGeQH4rzueiKSjt0ItMjISr732Gry9vUstF0IgPj4eAGBlZYWJEyfqa5NEJuHczUxcTM6ClaUcA5p63/8BRDVM+4Phj1OJKChSSxwNkXnTW6EWEhKC1NTUMsvT0tIQFBSkr80QmRxtq0WvUE842SokjoYI6FjPDZ6OSqTnqrDrAq/YJ5KS3gq1ik46zc7OhrU15yskKk+RWoPfo4sLtUdb8iICMgwWcpluqA5OKUUkLcvqPsHMmTMBFA+WOGfOHNja2uruU6vVOHToEMLDw6u7GSKTFBWTitTsQrjZW6FzfXepwyHSGR7hh+/+vYpdF1KQllMIFzsrqUMiMkvVLtROnDgBoLhF7fTp07Cy+u/DbGVlhebNm2PWrFnV3QyRSfr1bmvF4Oa+UFjofbQcoofW0MsBTXwdcSYhE3+cTMTEDnWlDonILFW7UNu1axcAYPLkyfjyyy/h6OhY7aCIzEFGngqR55IBcOw0MkyPtvDDmYRz2HD8Bgs1Iono7Sf80qVLWaQRVcHW0zdRWKRBQ08HhPnws0OGZ1BzH1jKZTh5IwOXU7KkDofILFWrRW348OFYtmwZHB0dMXz48ErX3bBhQ3U2RWRytBNfD2/hC5mMU0aR4XGzV6JbQ3dsP5+C344n4LW+jaQOicjsVKtFzcnJSfcF4+TkVOkfEf0n7nYOjsTegVz230TYRIZIO6baphMJUGs4pRRRbatWi9rSpUvL/T8RVW7j3QmvO9V3h6cjh68hw9Uj1AOO1pa4mZGPg1dvo2M9N6lDIjIrejtHLS8vD7m5ubrbcXFxWLhwIf755x99bYLIJAghdIPcPsqLCMjAKS0tMKi5DwDgt2McU42otumtUBsyZAh+/vlnAEB6ejratGmDzz//HEOGDMHixYv1tRkio3ck9g7i03JhZ2WB3o29pA6H6L603Z9/nUlCTkGRxNEQmRe9FWrHjx9H586dAQC//vorvLy8EBcXh59//hlfffWVvjZDZPTWH70OABjYzAc2VhYSR0N0fy0CnFHX1RZ5KjX+PpMkdThEZkVvhVpubi4cHBwAAP/88w+GDx8OuVyOdu3aIS4uTl+bgVqtxttvv42goCDY2NggJCQE7733XoVTWBEZkpyCImw5fRMAMLKVn8TRED0YmUyma1XjlFJEtUtvhVq9evWwadMmXL9+Hdu2bUPv3r0BACkpKXodX23+/PlYvHgxvv76a5w/fx7z58/HJ598gkWLFultG0Q1Zevpm8gtVCPIzQ4tA+tIHQ7RAxt29+rkA1dvIyE9T+JoiMyH3gq1OXPmYNasWahbty7atm2L9u3bAyhuXYuIiNDXZrB//34MGTIEAwYMQN26dTFixAj07t0bhw8f1ts2iGrK+rsnY49o6cex08io+LvYom2QC4QANvCiAqJao7dCbcSIEYiPj8fRo0fx999/65b36NEDX3zxhb42gw4dOmDHjh24dOkSAODkyZPYu3cv+vXrp7dtENWEuNs5OHwtDXIZp4wi4zSqlT+A4h8cGo6pRlQrqj3XZ0leXl7w8ip9FVubNm30uQm8/vrryMzMRKNGjWBhYQG1Wo0PPvgA48aNK3f9goICFBQU6G5nZmYCAFQqFVQqlW659v8ll5k6c8tZ6nzXHo4HAHQMcYWbrWWtxCF1zrXN3PIFajfnno1cYae0QHxaLvZfTkHbIJca3+a9uI/NQ3k5m1P+JcmEns7Cz8nJwccff4wdO3YgJSUFGo2m1P1Xr17Vx2awZs0avPLKK/j0008RFhaG6OhozJgxAwsWLMDEiRPLrD937lzMmzevzPJVq1bB1tZWLzER3Y9GAPOOWyC9UIaJ9dVo4cbWCDJOa67IcSBFjtbuGjxeT3P/BxDpSW5uLsaOHYuMjAyzmltcb4XamDFj8O+//2L8+PHw9vYuc/7Niy++qI/NwN/fH6+//jqeffZZ3bL3338fK1aswIULF8qsX16Lmr+/P1JTU0vtaJVKhcjISPTq1QsKhUIvsRo6c8tZynz3XbmNScuOwdHaEvtf7QqlonaG5eA+Nn21nfPx+HQ8tuQwbBRy7H+tG+yVeu2YuS/uY/PNOTMzE25ubmZXqOntE/bXX39hy5Yt6Nixo76esly5ubmQy0ufWmdhYVGmBU9LqVRCqVSWWa5QKMp9w1e03JSZW85S5LsxunhIjsHhPrC3rf0po7iPTV9t5dwm2A3B7na4eisH/5y/hcdaB9T4NsvDfWweSuZsbrlr6e1igjp16sDFpebPVxg0aBA++OADbNmyBbGxsdi4cSMWLFiAYcOG1fi2iR5GRp5KN0joyJb+EkdDVD0ymUz3Pl53lFd/EtU0vRVq7733HubMmVNqvs+asGjRIowYMQLTp09HaGgoZs2ahaeffhrvvfdejW6X6GH9eSoRBUUaNPC0RzM/J6nDIaq2R1v4wkIuw7G4O7hyK1vqcIhMmt66Pj///HNcuXIFnp6eqFu3bpkmyuPHj+tlOw4ODli4cCEWLlyol+cjqmnr77Y6jGzpz7HTyCR4OFqjawN37LyQgvVHb+D1fo2kDonIZOmtUBs6dKi+norIZFxOyUL09XRYyGUYGsGx08h0jGrlh50XUrDh+A3M6t0AlhZ666AhohL0Vqi98847+noqIpOhbU3r3tAd7g5lL2ohMlaPNPKEi50VUrIKsCfmFh5p5Cl1SEQmSa8/gdLT0/HDDz9g9uzZSEtLA1Dc5ZmQkKDPzRAZhSK1BhtOFL/3R/AiAjIxVpZyDA0vbiVez4sKiGqM3gq1U6dOoUGDBpg/fz4+++wzpKenAwA2bNiA2bNn62szREZjT8wt3MoqgIudFR5p5CF1OER6N6q1HwBg+/lkpOUUShwNkWnSW6E2c+ZMTJo0CTExMbC2/m+cqP79+2PPnj362gyR0dC2MgwN94WVJc/fIdPTyMsRTX2doFILbDrBnhOimqC3b48jR47g6aefLrPc19cXSUlJ+toMkVFIzS7A9vPJAICRrfwkjoao5oy6+/5ed/Q69DTRDRGVoLdCTalU6iY8L+nSpUtwd3fX12aIjMLG4wlQqQWa+zkh1Nt8pjoh8zO4eXGL8YWkLJxNLPsdQETVo7dCbfDgwXj33Xd1s9vLZDLEx8fjtddew6OPPqqvzRAZPCEE1hyJBwDJptchqi1Otgr0CfMCUNyqRkT6pbdC7fPPP0d2djbc3d2Rl5eHrl27ol69enBwcMAHH3ygr80QGbyjcXdw5VYObBQWGNTcW+pwiGrcyJbF3Z+/RyciX6WWOBoi06K3cdScnJwQGRmJffv24eTJk8jOzkaLFi3Qs2dPfW2CyCisOVzcqjCouTccrM1zEmEyLx3rucHX2QYJ6Xn4+0wSB3cm0iO9FGoajQbLli3Dhg0bEBsbC5lMhqCgIHh5eUEIwWlzyGxk5quw5XQiAHZ7kvmwkMswqpU/vth+CasPx7NQI9Kjand9CiEwePBgPPnkk0hISEDTpk0RFhaGuLg4TJo0CcOGDdNHnERGobjrR4P6HvZoEeAsdThEtWZUaz/IZcCha2mcqJ1Ij6pdqC1btgx79uzBjh07cOLECaxevRpr1qzByZMnsX37duzcuRM///yzPmIlMnhr715EMLpNAFuSyax4O9mge8PigZ3XHuFFBUT6Uu1CbfXq1XjjjTfQvXv3Mvc98sgjeP3117Fy5crqbobI4J1JyMCZhExYWcgxjF0/ZIZGtynu7v/12A0UFPGiAiJ9qHahdurUKfTt27fC+/v164eTJ09WdzNEBk/bitA7rHiyaiJz072hOzwdlUjLKUTkuWSpwyEyCdUu1NLS0uDp6Vnh/Z6enrhz5051N0Nk0PIK1dgUXTyFzpg2vIiAzJOlhRwjW/oD+O/qZyKqnmoXamq1GpaWFV88amFhgaKioupuhsigbT19E1n5RfB3sUH7YFepwyGSzGOt/SGTAXsvpyL+dq7U4RAZvWoPzyGEwKRJk6BUKsu9v6CgoLqbIDJ42m7Px1r5Qy7nRQRkvvxdbNGpnhuiYlKx9mg8XunTSOqQiIxatQu1iRMn3nedCRMmVHczRAbrcko2DsemQS4DRrbylzocIsmNaROAqJhUrDt6AzN6NoDCQm+T4BCZnWoXakuXLtVHHERGSzu/4SONPODpaC1xNETS6xnqCVc7K9zKKsDOCym6uUCJqOr4M4eoGgqK1Fh/t1DjTARExaws5RjRqnj+zzWH4yWOhsi4sVAjqoa/TifhTq4K3k7W6N7QXepwiAzG6Ls/XHZfuoWE9DyJoyEyXizUiKphxcE4AMXn5FjyPBwinSA3O7QLdoEQwDrOVED00PjNQvSQLiRl4mjcHVjIZRjdmhcREN1LO6bg2iPXUaTWSBwNkXFioUb0kFYeLD73pndjT3jwIgKiMvo28YKLnRWSMvOx40KK1OEQGSUWakQPIaegCBtPFM9E8Hi7QImjITJMSksLjLo7ZI32NAEiqhoWakQP4ffoRGQXFCHYzQ4dQjgTAVFFxrUNgEwGRMWk4uqtbKnDITI6LNSIqkgIoWsdGNs2ADIZZyIgqoi/iy26N/QAAKw8xKE6iKqKhRpRFZ24no5zNzOLx4pq6Sd1OEQGb/zd0wPWH72OvEK1xNEQGRcWakRVpL2IYGAzbzjbWkkcDZHh69LAHf4uNsjML8IfJxOlDofIqLBQI6qC9NxC/Hmq+IuGFxEQPRgLuQzj2hZ/XlYc4kUFRFXBQo2oCn49dgMFRRo09nZEhL+z1OEQGY1RrfxhZSnHqRsZOHk9XepwiIyGURZqCQkJePzxx+Hq6gobGxs0bdoUR48elTosMnFCCN3J0OPa8SICoqpwsbPCwKbeAIBfOFQH0QMzukLtzp076NixIxQKBf766y+cO3cOn3/+OerUqSN1aGTi9l5OxbXUHNgrLTEk3FfqcIiMzuPti7s//ziZiDs5hRJHQ2QcLKUOoKrmz58Pf39/LF26VLcsKChIwojIXCzbFwsAGNHSD/ZKo/voEEkuwt8Zjb0dce5mJn49dgNPdQmWOiQig2d03zabN29Gnz59MHLkSPz777/w9fXF9OnT8dRTT5W7fkFBAQoKCnS3MzMzAQAqlQoqlUq3XPv/kstMnbnlXJ1849JysfNi8RQ4Y1v7Gs1rxn1s+owt57Ft/PDW7+fwy8FYTGjrB7m8aqcQGFu++sCcUeb/5kQmhBBSB1EV1tbFcyrOnDkTI0eOxJEjR/Diiy/i22+/xcSJE8usP3fuXMybN6/M8lWrVsHW1rbG4yXTsDFWjt035Qh11mBaKCeXJnpYBWpgzjEL5KtlmNZIjdA6RvUVRBLKzc3F2LFjkZGRAUdHR6nDqTVGV6hZWVmhVatW2L9/v27ZCy+8gCNHjuDAgQNl1i+vRc3f3x+pqamldrRKpUJkZCR69eoFhUJRs0kYCHPL+WHzzSkoQufP9iArvwg/jI9A1wbuNRilfnEfmz5jzPmDrRew7EA8utR3xY8TWlbpscaYb3Ux5+KcMzMz4ebmZnaFmtF1fXp7e6Nx48alloWGhuK3334rd32lUgmlUllmuUKhKPcNX9FyU2ZuOVc13z+OJSIrvwhBbnZ4JNS7yl01hoD72PQZU85PdArB8oPx2BNzG3F3ClDPw77Kz2FM+eqLuedsbrlrGd1Vnx07dsTFixdLLbt06RICAzn4KOmfEALL98cCACa0DzTKIo3I0AS42qJHI08A0H2+iKh8RleovfTSSzh48CA+/PBDXL58GatWrcL333+PZ599VurQyATtu3wbl1OyYWdlwXk9ifToiY51AQC/Hb+BjDzzPEmc6EEYXaHWunVrbNy4EatXr0aTJk3w3nvvYeHChRg3bpzUoZEJWrb/GoDiITkcrM2z2Z2oJrQPcUVDTwfkFqqx7sh1qcMhMlhGV6gBwMCBA3H69Gnk5+fj/PnzFQ7NQVQd8bdzseNC8ZAcEzrUlTYYIhMjk8kw+W6r2vIDsVBrjOq6NqJaY5SFGlFt+PlALIQAujRwR4h71U92JqLKDY3whbOtAjfu5CHyXLLU4RAZJBZqROXIKSjC2qPF3TGT2ZpGVCOsFRYY0yYAALB03zWJoyEyTCzUiMqx/uh1ZOUXoa6rrVGNm0ZkbMa3C4SFXIZD19JwNjFD6nCIDA4LNaJ7qDUCP92d13NKpyAOyUFUg3ycbdC3iReA/+bTJaL/sFAjusc/Z5MQn5YLZ1sFRrT0lzocIpOnHarj95OJSM0uqHxlIjPDQo3oHkuirgIAHm8bCBsrC4mjITJ9LQLqoLmfEwqLNPj5QJzU4RAZFBZqRCUci7uD4/HpsLKQY0IHznZBVBtkMhme6hIMAPjlQCzyCtUSR0RkOFioEZXww93WtCHhPvBwsJY4GiLz0TfMC/4uNriTq8KvxzgALpEWCzWiu+Jv52Lb2SQAwJOdgyWOhsi8WFrIMaVjEADgh73XOAAu0V0s1Iju+mnfNWjuDnDb0MtB6nCIzM6o1v5wtlUg7nYu/rn7o4nI3LFQIwKQkavCursD3D7VOUjiaIjMk62VJca3Kz439Ls9VyEEW9WIWKgRAVh5OA65hWo08nJAp3puUodDZLYmtK8LK0s5oq+n40jsHanDIZIcCzUye/kqNX7aGwsAeKpzMGQyDnBLJBV3ByUebeELAPh+z1WJoyGSHgs1Mnvrj91AanYBfJ1tMDjcR+pwiMzek52DIZMB288n43JKttThEEmKhRqZtSK1Bt/vuQIAmNolGAoLfiSIpBbibo+eoZ4AgCVsVSMzx28lMmt/nrqJ62l5cLWzwqhWnC6KyFBM61o8RM6GEzdwMyNP4miIpMNCjcyWRiOweHdxa9oTnYI4XRSRAWkZ6IK2QS5QqQW++5etamS+WKiR2dp5IQUXk7Ngr7TE4+04XRSRoXnukXoAgDVH4jlZO5ktFmpkloQQ+N/uywCAx9sFwslGIXFERHSvTvXc0NzPCfkqDX7ce03qcIgkwUKNzNKha2nFk69byvFEp7pSh0NE5ZDJZHi2e3Gr2i8H4pCRq5I4IqLax0KNzNL/7p6bNqqVHydfJzJgPUM90dDTAdkFRVh+IFbqcIhqHQs1MjunEzKw59ItWMhleLpLiNThEFEl5HIZpncv/pz+tO8acgqKJI6IqHaxUCOzs2hXcWvakHAf+LvYShwNEd3PwGY+qOtqi/RcFdYcvSF1OES1ioUamZX4bGDXxVRYyGV44ZH6UodDRA/AQi7DM92KW9V+3BsLlUbigIhqEQs1Mit/XS9+yw8N90VdNzuJoyGiBzUswg8+Tta4lV2IA8mcj5fMBws1MhunbmTgXLocFnIZnr87PhMRGQcrSzmm370CNDJBjrxCtcQREdUOFmpkNrTnpg1u7s3WNCIjNKqVP3ydrZGpkmH1ketSh0NUK1iokVk4eT0duy+lQg6BZ+/OIUhExsXKUo5nuxV/fr+L4hWgZB5YqJFZ+HJHDACglbtAoCuv9CQyVkPDfeCmFEjLUeHnA3FSh0NU41iokck7eT0dOy+kwEIuQ29fXi5GZMwUFnL08S/+HH+35wqy8jlbAZk2Fmpk8hZEXgJQfG6au43EwRBRtbV0Ewi6O67asn2xUodDVKOMvlD7+OOPIZPJMGPGDKlDIQN04Mpt/HvpFizlMt25LURk3CxkwPOPFI+rtiTqKjLy2KpGpsuoC7UjR47gu+++Q7NmzaQOhQyQEAKfbLsAABjTJgCBnIWAyGT0b+KF+h72yMwvwo9RV6UOh6jGGG2hlp2djXHjxmHJkiWoU6eO1OGQAYo8l4wT8emwUVhw3DQiE2Mhl+GlXg0AAD/uvYZbWQUSR0RUMyylDuBhPfvssxgwYAB69uyJ999/v8L1CgoKUFDw3wc4MzMTAKBSqaBS/ddcrv1/yWWmzpRzVmsEPr3bmjapfQDq2FiYdL4VMbeczS1fwPxyLplvjwauaOrriNMJmfhq+0XMGRgqcXQ1w9z2MVB+zuaUf0kyIYSQOoiqWrNmDT744AMcOXIE1tbW6NatG8LDw7Fw4cIy686dOxfz5s0rs3zVqlWwtWVXmKk6fEuGlZctYGsh8HYLNWyN9icJEVUmJkOGr89ZQC4TeKO5mhcMmbDc3FyMHTsWGRkZcHR0lDqcWmN0X1/Xr1/Hiy++iMjISFhbW993/dmzZ2PmzJm625mZmfD390fv3r1L7WiVSoXIyEj06tULCoWiRmI3NKaac0GRBp98uRdAPp7t0QAjOgcBMN18K2NuOZtbvoD55Vxevqd+PoY9MbdxosgPC/ub3jnL5raPgfJz1vaImRujK9SOHTuGlJQUtGjRQrdMrVZjz549+Prrr1FQUAALCwvdfUqlEkqlsszzKBSKct/wFS03ZaaW84rD15CQng9PRyWe6BQChcKi1P2mlu+DMLeczS1fwPxyLpnv6/0aI+pyFLacScLUriFo7u8sbXA1xNz2MVA6Z3PLXcvoLibo0aMHTp8+jejoaN1fq1atMG7cOERHR5cq0sj8ZOSp8NXdWQhe6FEfNlZ8PxCZusY+jhgW7gsA+PivCzDCM3qIKmR0LWoODg5o0qRJqWV2dnZwdXUts5zMz9c7Y3AnV4V6HvZ4rJW/1OEQUS2Z2bsB/jx1Eweu3saemFR0beAudUhEemF0LWpEFYm7nYNl+2MBAG8OCIWlBd/eRObCr44tJrQPBAB8tPU81Bq2qpFpMLoWtfLs3r1b6hDIAHz81wWo1AKd67uhG39NE5md5x6ph/XHbuBCUhbWHInHuLaBUodEVG1sciCTcPhaGv46kwS5rLg1TSaTSR0SEdUyZ1srvNSzPgDg838ucWopMgks1MjoaTQC7285BwB4rHUAGnmZz/g6RFTauHaBqOdhj7ScQt2FRUTGjIUaGb3fTybg1I0M2FlZYObdKWWIyDwpLOR4e2BjAMDy/bG4citb4oiIqoeFGhm17IIifPxX8VRR07vXg7tD2THziMi8dG3gjkcaeaBII/DBlvNSh0NULSzUyKgt2hGD5MwCBLjYYkqnIKnDISID8eaAUFjKZdh5IQX/XroldThED42FGhmtmOQs/Lj3GgBg7uDGsFZwcFsiKhbibo+JHeoCAN794ywKizTSBkT0kFiokVESQuCdzWdRpBHoGeqJRxp5Sh0SERmYF3rUh5u9Fa7cysGSqKtSh0P0UFiokVH689RN7L9yG0pLOd4Z1FjqcIjIADnZKPDmgFAAwKKdMbielitxRERVx0KNjE52QZFuOI7p3erB38VW4oiIyFANDfdFu2AX5Ks0eGfzWc4DSkaHhRoZnZIXEDzdNVjqcIjIgMlkMrw/tAkUFsUXFmw7myx1SERVwkKNjMrZxAz8cPcCgncG8QICIrq/eh4OeKpz8Y+6eX+cRU5BkcQRET04FmpkNIrUGrz+22moNQIDmnqjRygvICCiB/P8I/XhV8cGNzPy8SVnLCAjwkKNjMZP+67hdEIGHK0t8c5gXkBARA/OxsoC8waHAQB+3HsNp29kSBwR0YNhoUZGIe52DhZEXgIAvDWgMTwcrCWOiIiMTY9QTwxo5g21RuCVX09ybDUyCizUyOAJIfDGxtPIV2nQIcQVI1v5SR0SERmpeYPDUMdWgQtJWVi8+4rU4RDdFws1Mnjrj93AvsvFY6Z9NLwpZDKZ1CERkZFys1di7t0u0K93xeBCUqbEERFVjoUaGbSbGXl4/8/iMdNm9mqAQFc7iSMiImM3uLkPeoZ6QqUWePXXUyhSswuUDBcLNTJYQhQfRDPzi9Dcz4mTrhORXshkMnwwrAkcrS1x6sZ/Q/4QGSIWamSwfjkYh6iYVCgt5VjwWDgsLfh2JSL98HS0xtsDi68eXxB5CReTsiSOiKh8/OYjg3T1VjY+3HoeADC7XyOEuNtLHBERmZoRLf3wSCMPFBZp8OKaEygoUksdElEZLNTI4BSpNZi57iTyVRp0rOeKCe3rSh0SEZkgmUyG+Y82g6udFS4kZeGzbRelDomoDBZqZHAW776C6OvpcLC2xKcjmkMu51WeRFQz3B2UmP9oMwDAkqhr2Hc5VeKIiEpjoUYG5Xj8Hd30LvMGh8HH2UbiiIjI1PVs7ImxbQMAAC+vO4n03EKJIyL6Dws1MhgZuSo8v+oEijQCA5t5Y1iEr9QhEZGZeGtAKILd7JCUmY83Np6GEELqkIgAsFAjAyGEwKu/nURCeh4CXGw5sC0R1SpbK0ssHB0OS7kMW08nYcWheKlDIgLAQo0MxC8H47DtbDIUFjJ8PTYCDtYKqUMiIjPTzM8Zr/ZtCAB4749zOHUjXdqAiMBCjQzA2cQMvP9n8VAcr/VthGZ+ztIGRERm66nOwejV2BOFag2mrzyOjFyV1CGRmWOhRpJKzy3EtBXHUKjWoEcjD84+QESSkslk+Gxkc/i72ODGnTy8vP4kz1cjSbFQI8moNQIvronG9bQ8+LvY4PNRzXleGhFJzslGgcXjWsLKUo7t55Px/Z6rUodEZoyFGklm4fZL+PfSLVgr5Pju8VZwtrWSOiQiIgBAE18nvDOoeIqpT7Zd5PhqJBkWaiSJbWeTsGjnZQDAx8ObobGPo8QRERGVNrZNAIa38IVaI/DsquOIu50jdUhkhoyuUPvoo4/QunVrODg4wMPDA0OHDsXFi5z2w5hcSs7Cy+tOAgAmd6yLoRwvjYgMkEwmw4fDmqK5vzPSc1V4cvlRZOXz4gKqXUZXqP3777949tlncfDgQURGRkKlUqF3797IyeEvHWNwK6sAk5ceQXZBEdoGueCN/qFSh0REVCFrhQW+H98Sno5KxKRkY8aaaKg1vLiAao/RFWp///03Jk2ahLCwMDRv3hzLli1DfHw8jh07JnVodB/5KjWe+vkoEtLzUNfVFt8+3hIKC6N7CxKRmfF0tMb341vBylKOHRdS8Mm2C1KHRGbEUuoAqisjIwMA4OLiUu79BQUFKCgo0N3OzMwEAKhUKqhU/zVha/9fcpmpq82cNRqBl9adQvT1dDjZWOL7xyNgbyWr1deb+9j0mVu+gPnlLFW+jb3s8OHQMMz69TS++/cqvB2sMO7u/KA1zdz2MVB+zuaUf0kyYcQDxGg0GgwePBjp6enYu3dvuevMnTsX8+bNK7N81apVsLW1rekQ6a4/4uXYniCHhUxgeqga9ZykjoiIqOr+vi7DXzcsIIPAlIYaNHUx2q9Qo5Obm4uxY8ciIyMDjo7mcwGaURdqzzzzDP766y/s3bsXfn5+5a5TXouav78/UlNTS+1olUqFyMhI9OrVCwqFeUxfVFs5LzsQhw+2Fl/w8fGwMDzaQpqLB7iPTT9nc8sXML+cpc5XCIE3fz+H9ccSYK2Q45fJrRDu71yj25Q6ZymUl3NmZibc3NzMrlAz2q7P5557Dn/++Sf27NlTYZEGAEqlEkqlssxyhUJR7hu+ouWmrCZz3nQiQVekvdyrAUa3rVsj26kK7mPTZ275AuaXs5T5fji8GW5lF2L3xVt4emU01k9rjxB3+xrfrrntY6B0zuaWu5bRnckthMBzzz2HjRs3YufOnQgK4pRDhmrXxRTMWl88DMekDnXx3CP1JI6IiKj6FBZyfDO2BZr6OiEtpxCP/3AI19NypQ6LTJTRFWrPPvssVqxYgVWrVsHBwQFJSUlISkpCXl6e1KFRCUdi0/DMimMo0ggMDffBnIGNOT0UEZkMO6Ullk1ujXoe9riZkY9xPxxCUka+1GGRCTK6Qm3x4sXIyMhAt27d4O3trftbu3at1KHRXUdj0zDpp8PIV2nQraE7Ph3ZHHI5izQiMi2u9kqsmNIWAS62iE/LxbgfDuJ2dsH9H0hUBUZXqAkhyv2bNGmS1KERgGNxaZj402HkFKrRqZ4bx0ojIpPm5WSNlU+2hbeTNa7cysG4Hw6xWCO94jco6c3x+DuY+NMR5BSq0SHEFUsmtIK1wkLqsIiIapS/iy1WPtkW7g5KXEjKwujvDyIli92gpB8s1EgvDl69jQk/HkZ2QRHaB7vix4mtYWPFIo2IzEOwuz3WTm0HL0drxKRkY/R3B3Ezg+dOU/WxUKNq234uGRN+KlGkTWrFIo2IzE6wuz3WPd0evs42uJqag1HfHeDVoFRtLNSoWjaeuIGnVxxDYZEGPUM9sXRya9haGe3wfERE1RLgaou1T7dDoKstrqflYfji/TibmCF1WGTEWKjRQxFC4Ieoq3hp7UmoNQLDI3zx7eMteE4aEZk9vzq2WPd0ezTycsCtrAI89t1B7LucKnVYZKRYqFGVFak1mPP7Wby/5TyA4sFsPxvZHJa8upOICADg6WiNddPao12wC7ILijBp6WFsOpEgdVhkhPjNSlWSla/ClOVH8cvBOMhkwJv9Q/HOoMYcJ42I6B6O1gosf6INBjbzhkotMGNtNBb8cxEajdFOsU0SYKFGDyz+di5GfnsA/166BWuFHN8+3hJPdQnmjANERBVQWlrgq9ERmNolGADw1c7LeHrFMWQXFEkcGRkLFmr0QHZeSMbARVG4kJQFdwcl1j3dHn3CvKQOi4jI4MnlMrzRPxSfj2wOK0s5Is8lY/j/9iHudo7UoZERYKFGlVJrBBZEXsITy44iM78IEQHO2PxcRzTzc5Y6NCIio/JoSz+sndoOHg5KXErOxuCv9yHyXLLUYZGBY6FGFUrNLsDkZUfw1Y4YAMCE9oFYO7U9vJ1sJI6MiMg4RQTUwR/Pd0K4vzMy8lR46uejmPfHWRQUqaUOjQwUCzUq164LKei7cA/23D0fbcGo5nh3SBNYWfItQ0RUHZ6O1lj3dHtM6RQEAFi6LxYjFh9AbCq7QqksfutSKXmFary96QwmLzuC1OxCNPC0x8bpHTG8hZ/UoRERmQwrSzneHtgYP05sBWdbBU4nZGDgor1YczgeQvCqUPoPCzXSOR5/B4O+3otfDsYBACZ3rIvNz3VCqLejxJEREZmmHqGe+OvFzmhTt3i8tdc3nMaEnw4jIZ3zhFIxFmqE7IIivPP7GTy6eD8up2TDw0GJn59og3cGhXGmASKiGubtZIPVU9vhzf6hUFrKERWTij5f7GHrGgFgoWb2TqfJ0O+rfVh+IA5CAI+28MO2GV3QpYG71KEREZkNC7kMT3UJxtYXO6NFgLOudW3UdwdwISlL6vBIQpw920xduZWN9/44i92XLAAUIMDFFh8Oa4pO9d2kDo2IyGyFuNtj/bQO+GnvNSyIvIQjsXcwdPFBdPSQo1OeCq4KhdQhUi1ji5qZychV4d0/zqHPF3uw+1Iq5DKBpzrVxbYZXVikEREZAG3r2o6Xu2JAU2+oNQJ7kuTo/eU+rDgYB5VaI3WIVIvYomYm8grVWHEwDv/bfRl3clUAgO4N3dDeJgmT+zSAgueiEREZFB9nG3wzrgVGXkjCq2uOIiWnEG9tOoMf917DrN4N0b+pF6fwMwMs1ExcvkqN1Yfj8b/dV3ArqwAA0MDTHm8NaIz2Qc7YunWrxBESEVFlOoa44rXmamS4NcE3u6/iWmoOnl11HM38nDCjZ310b+jBgs2EsVAzUdkFRVh35DqWRF3FzYx8AIBfHRu80KM+hkf4wtJCDpVKJXGURET0ICzlwPh2ARjVJhBL9lzFkqirOHUjA08sO4rG3o54tns99G3iBQs5CzZTw0LNxCRl5GPZ/lisPBSHrPwiAIC3kzWee6QeRrb058wCRERGzF5piZd6NcDj7QKxJOoqVhyMw7mbmXh21XEEu9thSqcgDIvwha0Vv95NBfekCRBC4FjcHaw6FI8/TiVCpS4edyfYzQ5TOgfh0RZ+HA+NiMiEuDso8Ub/UDzTNQRL98di2b5ruHorB29uPIP5f13AqFb+mNC+LgJcbaUOlaqJhZoRu5NTiA0nErD6cDwup2Trlrep64KnugSjRyMPyNkMTkRksurYWWFmrwZ4qnMQ1h65jl8OxiHudi5+2HsNP+67hq4N3DGipR96hnryB7uRYqFmZPJVauy8kILN0YnYeTEFhUXFl2nbKCwwsJk3xrULRLi/s7RBEhFRrXKwVuDJzsF4omMQ/r10C8sPxGL3xVu6P0drSwxs7oNHW/ihRYAzLz4wIizUjEC+So19l1Pxx8lERJ5LRk6hWndfY29HjG0bgMHhPnC05kCIRETmTC6XoXsjD3Rv5IHY1Bz8euwGNhy/gcSMfKw6FI9Vh+Lh62yDvk280LeJF1oE1OEFCAaOhZqBSs7Mx64LKdhxIQV7Y1KRp/qvOPOrY4NBzX0wsJk3Gns78pcRERGVUdfNDrP6NMTMXg1w4Opt/HbsBv46k4SE9Dz8uPcaftx7DW72SvQO80T3hh5oH+IKeyXLAkPDPWIgsvJVOBp3Bwev3sa+y6k4k5BZ6n4vR2v0a+qFQc19EOHPZmsiInowcrkMHeu5oWM9N3wwTI09Mbew7UwSIs8nIzW7QNfSprCQoUVAHXRp4I7O9d0Q5uPE1jYDwEJNIimZ+Th5IwNH49Jw8GoaziRkQK0RuvtlMiDc3xmPNPTAI6EebDkjIqJqs7GyQJ8wL/QJ80JhkQYHrt5G5LkkRMWkIu52Lg5dS8Oha2n4dNtF2CstERHgjFaBLmhVtw7C/Z1hxxa3WsdXvBak5RTiXGImTt5Ix6kb6Th5PQNJmfll1gt0tUW7IFe0C3FB5/rucLNXShAtERGZAytLObo2cEfXBu4AgLjbOdgTk4o9l27h4JXbyCooQlRMKqJiUgEUz0HawNMBYT6OCPNxRBNfJ4R6O7K7tIbx1dWj9NxCXErOxqXkLMQkZ+FScjZiUrKQml1YZl25DKjnYY8I/zpoF+KCtkGu8HG2kSBqIiIiINDVDuNd7TC+XSDUGoFLyVk4GpuGo3F3cDT2DhLS83D+ZibO38zEr8eKHyOTAXVd7dDQ0wH1POxR39MeIe7FfzZWHA5EH4y2UPvmm2/w6aefIikpCc2bN8eiRYvQpk0byeI5fSMDg77eW+H9AS62aObnhOZ+zmjm54Qmvk5sQiYiIoNkIZch1NsRod6OGN++LgDgZkYeTt/IwNnETJxNLP73ZkY+rqXm4FpqDnD2v8c7KC1xam5vnrKjB0ZZKaxduxYzZ87Et99+i7Zt22LhwoXo06cPLl68CA8PD0liCna3g0wG+DjZoL6nPRp4Otz9s0c9D3tO50FEREbN28kG3k426B3mpVt2O7sAZxMzEZOSjcsp2bickoWYlGwEutiySNMTo6weFixYgKeeegqTJ08GAHz77bfYsmULfvrpJ7z++uuSxGSntMSZuX3YSkZERGbD1V6JLg3c0eXueW5A8bSGJYeUouoxuhm6CwsLcezYMfTs2VO3TC6Xo2fPnjhw4ICEkYFFGhERmT2ZTMZeJD0yulcyNTUVarUanp6epZZ7enriwoULZdYvKChAQUGB7nZmZvH4ZCqVCiqVSrdc+/+Sy0ydueVsbvkC5pezueULmF/O5pYvwJzvXWZuZEIIcf/VDEdiYiJ8fX2xf/9+tG/fXrf81Vdfxb///otDhw6VWn/u3LmYN29emedZtWoVbG1tazxeIiIiqr7c3FyMHTsWGRkZcHR0lDqcWmN0LWpubm6wsLBAcnJyqeXJycnw8vIqs/7s2bMxc+ZM3e3MzEz4+/ujd+/epXa0SqVCZGQkevXqBYXCPObMNLeczS1fwPxyNrd8AfPL2dzyBZizNmdtj5i5MbpCzcrKCi1btsSOHTswdOhQAIBGo8GOHTvw3HPPlVlfqVRCqSw7cKxCoSj3DV/RclNmbjmbW76A+eVsbvkC5pezueULMGdzy13L6Ao1AJg5cyYmTpyIVq1aoU2bNli4cCFycnJ0V4ESERERmQKjLNQee+wx3Lp1C3PmzEFSUhLCw8Px999/l7nAgIiIiMiYGWWhBgDPPfdcuV2dRERERKbC6MZRIyIiIjIXLNSIiIiIDBQLNSIiIiIDxUKNiIiIyECxUCMiIiIyUCzUiIiIiAyU0Q7P8bC0U5veOxWFSqVCbm4uMjMzzWb0Y3PL2dzyBcwvZ3PLFzC/nM0tX4A53zuFlJFNUV5tZleoZWVlAQD8/f0ljoSIiIiqKisrC05OTlKHUWtkwsxKU41Gg8TERDg4OEAmk+mWaydrv379eqnJ2k2ZueVsbvkC5pezueULmF/O5pYvwJy1OQshkJWVBR8fH8jl5nPmltm1qMnlcvj5+VV4v6Ojo9l8ELTMLWdzyxcwv5zNLV/A/HI2t3wB5gzArFrStMynJCUiIiIyMizUiIiIiAwUC7W7lEol3nnnHSiVSqlDqTXmlrO55QuYX87mli9gfjmbW74AczZ3ZncxAREREZGxYIsaERERkYFioUZERERkoFioERERERkoFmpEREREBsokC7W5c+dCJpOV+mvUqNEDPXbNmjWQyWQYOnSobplKpcJrr72Gpk2bws7ODj4+PpgwYQISExNrKIOq03fO95o2bRpkMhkWLlyon4CrqabyPX/+PAYPHgwnJyfY2dmhdevWiI+P13P0D6cmcs7OzsZzzz0HPz8/2NjYoHHjxvj2229rIPqqq2q+y5YtK7O+tbV1qXWEEJgzZw68vb1hY2ODnj17IiYmpqZTeWD6ztnQj101sY9LMrTjFlBzORvqsasm8jXk41ZNMNmZCcLCwrB9+3bdbUvL+6caGxuLWbNmoXPnzqWW5+bm4vjx43j77bfRvHlz3LlzBy+++CIGDx6Mo0eP6j32h6XPnEvauHEjDh48CB8fH73EqS/6zvfKlSvo1KkTpkyZgnnz5sHR0RFnz56t9Iugtuk755kzZ2Lnzp1YsWIF6tati3/++QfTp0+Hj48PBg8erNfYH0ZV83V0dMTFixd1t0tOEwcAn3zyCb766issX74cQUFBePvtt9GnTx+cO3fOYPazPnM2hmOXvvexlqEetwD952zoxy5952voxy19M9lCzdLSEl5eXg+8vlqtxrhx4zBv3jxERUUhPT1dd5+TkxMiIyNLrf/111+jTZs2iI+PR0BAgL7CrhZ95qyVkJCA559/Htu2bcOAAQP0GG316TvfN998E/3798cnn3yiWxYSEqKvcPVC3znv378fEydORLdu3QAAU6dOxXfffYfDhw8bxAGvqvnKZLIK1xdCYOHChXjrrbcwZMgQAMDPP/8MT09PbNq0CaNHj9ZLzNWlz5yN4dilz3y1DPm4Beg/Z0M/duk7X0M/bumbSXZ9AkBMTAx8fHwQHByMcePG3bcJ+N1334WHhwemTJnyQM+fkZEBmUwGZ2dnPUSrH/rOWaPRYPz48XjllVcQFhZWEyFXiz7z1Wg02LJlCxo0aIA+ffrAw8MDbdu2xaZNm2oo+oej733coUMHbN68GQkJCRBCYNeuXbh06RJ69+5dE+FXWVXzzc7ORmBgIPz9/TFkyBCcPXtWd9+1a9eQlJSEnj176pY5OTmhbdu2OHDgQI3lUFX6zLk8hnbs0ne+hn7cAvSbszEcu/S9jw39uKV3wgRt3bpVrFu3Tpw8eVL8/fffon379iIgIEBkZmaWu35UVJTw9fUVt27dEkIIMXHiRDFkyJAKnz8vL0+0aNFCjB07tibCfyg1kfOHH34oevXqJTQajRBCiMDAQPHFF1/UZBoPTN/53rx5UwAQtra2YsGCBeLEiRPio48+EjKZTOzevbs2UrqvmtjH+fn5YsKECQKAsLS0FFZWVmL58uU1ncoDqWq++/fvF8uXLxcnTpwQu3fvFgMHDhSOjo7i+vXrQggh9u3bJwCIxMTEUo8bOXKkGDVqVI3n8yD0nfO9DO3YVRP5GvJxSwj952zox66a2MeGfNyqCSZZqN3rzp07wtHRUfzwww9l7svMzBR169YVW7du1S2rrFArLCwUgwYNEhERESIjI6OmQq626uZ89OhR4enpKRISEnTLDO2AV1J1801ISBAAxJgxY0o9dtCgQWL06NE1Fnd16ON9/emnn4oGDRqIzZs3i5MnT4pFixYJe3t7ERkZWdPhV1ll+ZansLBQhISEiLfeeksIYRyF2r2qm/O99xn6sau6+RrbcUuI6udsbMcufbynjem4pQ8me45aSc7OzmjQoAEuX75c5r4rV64gNjYWgwYN0i3TaDQAivvVL168qOvrV6lUGDVqFOLi4rBz5044OjrWTgIPobo5R0VFISUlpdQ5LGq1Gi+//DIWLlyI2NjYGs+hKqqbr7+/PywtLdG4ceNSjw0NDcXevXtrNviHVN2cfXx88MYbb2Djxo2683iaNWuG6OhofPbZZ6W6CA1BZfmWR6FQICIiQre+9pyX5ORkeHt769ZLTk5GeHi43uPVh+rmrGUsx67q5mtsxy2g+jm7ubkZ1bGruvnm5eUZ1XFLH0z2HLWSsrOzceXKlVIHZ61GjRrh9OnTiI6O1v0NHjwY3bt3R3R0NPz9/QH8d6CLiYnB9u3b4erqWttpVEl1cx4/fjxOnTpVah0fHx+88sor2LZtmwQZVa66+VpZWaF169alrjQCgEuXLiEwMLC20qiS6uasUqmgUqkgl5c+DFhYWOiKOkNSWb7lUavVOH36tG79oKAgeHl5YceOHbp1MjMzcejQIbRv375GYq6u6uYMGNexq7r5GttxC6h+zsZ27KpuvsZ23NILqZv0asLLL78sdu/eLa5duyb27dsnevbsKdzc3ERKSooQQojx48eL119/vcLH39tFVFhYKAYPHiz8/PxEdHS0uHnzpu6voKCgptN5IPrOuTyG1IVQE/lu2LBBKBQK8f3334uYmBixaNEiYWFhIaKiomoylQdWEzl37dpVhIWFiV27domrV6+KpUuXCmtra/G///2vJlN5IFXNd968eWLbtm3iypUr4tixY2L06NHC2tpanD17VrfOxx9/LJydncXvv/8uTp06JYYMGSKCgoJEXl5eredXHn3nbOjHrprYx/cypOOWEDWTsyEfu2oiX0M+btUEk+z6vHHjBsaMGYPbt2/D3d0dnTp1wsGDB+Hu7g4AiI+PL1ONVyYhIQGbN28GgDJdJLt27dJdIiwlfeds6Goi32HDhuHbb7/FRx99hBdeeAENGzbEb7/9hk6dOtVEClVWEzmvWbMGs2fPxrhx45CWlobAwEB88MEHmDZtWk2kUCVVzffOnTt46qmnkJSUhDp16qBly5bYv39/qS6hV199FTk5OZg6dSrS09PRqVMn/P333wYz3pS+czb0Y1dN7GNDVxM5G/KxqybyNeTjVk2QCSGE1EEQERERUVmm08RCREREZGJYqBEREREZKBZqRERERAaKhRoRERGRgWKhRkRERGSgWKgRERERGSgWakREREQGioUaEZmEbt26YcaMGVKHQUSkVyzUiEhygwYNQt++fcu9LyoqCjKZDKdOnarlqIiIpMdCjYgkN2XKFERGRuLGjRtl7lu6dClatWqFZs2aSRAZEZG0WKgRkeQGDhwId3d3LFu2rNTy7OxsrF+/HkOHDsWYMWPg6+sLW1tbNG3aFKtXr670OWUyGTZt2lRqmbOzc6ltXL9+HaNGjYKzszNcXFwwZMgQxMbG6icpIiI9YKFGRJKztLTEhAkTsGzZMpScfnj9+vVQq9V4/PHH0bJlS2zZsgVnzpzB1KlTMX78eBw+fPiht6lSqdCnTx84ODggKioK+/btg729Pfr27YvCwkJ9pEVEVG0s1IjIIDzxxBO4cuUK/v33X92ypUuX4tFHH0VgYCBmzZqF8PBwBAcH4/nnn0ffvn2xbt26h97e2rVrodFo8MMPP6Bp06YIDQ3F0qVLER8fj927d+shIyKi6mOhRkQGoVGjRujQoQN++uknAMDly5cRFRWFKVOmQK1W47333kPTpk3h4uICe3t7bNu2DfHx8Q+9vZMnT+Ly5ctwcHCAvb097O3t4eLigvz8fFy5ckVfaRERVYul1AEQEWlNmTIFzz//PL755hssXboUISEh6Nq1K+bPn48vv/wSCxcuRNOmTWFnZ4cZM2ZU2kUpk8lKdaMCxd2dWtnZ2WjZsiVWrlxZ5rHu7u76S4qIqBpYqBGRwRg1ahRefPFFrFq1Cj///DOeeeYZyGQy7Nu3D0OGDMHjjz8OANBoNLh06RIaN25c4XO5u7vj5s2butsxMTHIzc3V3W7RogXWrl0LDw8PODo61lxSRETVwK5PIjIY9vb2eOyxxzB79mzcvHkTkyZNAgDUr18fkZGR2L9/P86fP4+nn34aycnJlT7XI488gq+//honTpzA0aNHMW3aNCgUCt3948aNg5ubG4YMGYKoqChcu3YNu3fvxgsvvFDuMCFERFJgoUZEBmXKlCm4c+cO+vTpAx8fHwDAW2+9hRYtWqBPnz7o1q0bvLy8MHTo0Eqf5/PPP4e/vz86d+6MsWPHYtasWbC1tdXdb2triz179iAgIADDhw9HaGgopkyZgvz8fLawEZHBkIl7T+IgIiIiIoPAFjUiIiIiA8VCjYiIiMhAsVAjIiIiMlAs1IiIiIgMFAs1IiIiIgPFQo2IiIjIQLFQIyIiIjJQLNSIiIiIDBQLNSIiIiIDxUKNiIiIyECxUCMiIiIyUCzUiIiIiAzU/wFdG0R5pSd7dAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "mean = 5.5\n", + "std_dev = 0.02483\n", + "\n", + "x = np.linspace(mean - 3 * std_dev, mean + 3 * std_dev, 1000)\n", + "pdf = 1/(std_dev * np.sqrt(2 * np.pi)) * np.exp(-(x - mean)**2 / (2 * std_dev**2))\n", + "\n", + "plt.plot(x, pdf)\n", + "plt.title(\"Normal Distribution with Mean = {} and Standard Deviation = {}\".format(mean, std_dev))\n", + "plt.xlabel('Value')\n", + "plt.ylabel('Density')\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c9305103-5f57-4459-aa01-b4b60dd53e29", + "metadata": {}, + "source": [ + "the experimentally obatained graph is nearly similar to the CLT obtained graph,the mean and variance are \n", + "nearly the same for both the graphs" + ] + }, + { + "cell_type": "markdown", + "id": "1ab391b5-fa99-4bc4-8593-c7d392a850b1", + "metadata": {}, + "source": [ + "**Question 5:**

\n", + "if X,Y are independent $P(X,Y)=P_{x}(X).P_{y}(Y)$
\n", + "so finding marginal pmf's
\n", + "marginal pmf of x:\n", + "$0\\leq y \\leq e^{-x}$
\n", + "$P_{x}(X=x)=\\int_{0}^{e^{-x}}1\\,dx=e^{-x}$

\n", + "marginal pmf of y:\n", + "$0\\leq x \\leq ln(\\frac{1}{y})$
\n", + "$P_{y}(Y=y)=\\int_{0}^{ln(\\frac{1}{y})}1\\,dx=ln\\frac{1}{y}$
\n", + "since $P(X,Y)\\neq P_{x}(X).P_{y}(Y)$ X,Y are not independent

\n", + "$P(Y|X)=\\frac{P(X,Y)}{P_{x}(X)}=\\frac{1}{e^{-x}}=e^x$

\n", + "intuitively we can see that the upper limit of y depends on what x is and threfore, for different values of x the probability of y will change, hence they seem to be dependent\n", + "

$$" + ] + }, + { + "cell_type": "markdown", + "id": "cc460f1a-c63d-4996-8468-33e98140a3b6", + "metadata": {}, + "source": [ + "
**Question 6:**

\n", + "$H_{0}:p=0.5$ against $H_{1}:p\\neq 0.5$
\n", + "given $\\bar{X}=4.97$
\n", + "$N=100$
\n", + "$\\mu=np=10(0.5)=5$
\n", + "$\\sigma^2=10(0.5)(0.5)=2.5$

\n", + "using normal approximation for binomial
\n", + "$Z=\\frac{\\bar{X}-\\mu}{\\frac{\\sigma}{\\sqrt{N}}}$

\n", + "$Z=\\frac{10(0.03)}{\\sqrt{2.5}}=-0.189$
\n", + "testing at 5% significance level
\n", + "$Z_{\\frac{\\alpha}{2}}=1.96$
\n", + "since $Z$ lies between $-Z_{\\frac{\\alpha}{2}}$ and $Z_{\\frac{\\alpha}{2}}$ the hypothesis is accepted\n", + "

\n", + "We don't take the null hypothesis as p=0.497 as it has no significance and gives no informtion in a general sense, taking hypothesis as p=0.5 gives information that the distribution can be number of successes on flipping a fair coin. We dont take the value based on the sample we instead use testing to check whether our assumption about the population is true.

" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e0185e7a-0ed0-40b7-b3ef-160a6ff791f8", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Assignment_5_(Q3,4,5).ipynb b/Assignment_5_(Q3,4,5).ipynb new file mode 100644 index 0000000..2feee01 --- /dev/null +++ b/Assignment_5_(Q3,4,5).ipynb @@ -0,0 +1,702 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "source": [ + "**Question 3:**" + ], + "metadata": { + "id": "T755viVhUrPu" + } + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "8nlCMzEGEtTh" + }, + "outputs": [], + "source": [ + "import torch\n", + "from torchvision import datasets, transforms\n", + "from torch.utils.data import Dataset,DataLoader\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "transform = transforms.Compose([\n", + " transforms.ToTensor(),\n", + " transforms.Normalize((0.1307,), (0.3081,))\n", + "])" + ], + "metadata": { + "id": "F9ABnIbTKSoi" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "train_dataset = datasets.MNIST(root='./data', train=True, transform=transform, download=True)\n", + "test_dataset = datasets.MNIST(root='./data', train=False, transform=transform, download=True)" + ], + "metadata": { + "id": "tEkTLRv3KVNL" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "train_loader = DataLoader(train_dataset, batch_size=64, shuffle=True)\n", + "test_loader = DataLoader(test_dataset, batch_size=1000, shuffle=False)" + ], + "metadata": { + "id": "10OwTCfiKya1" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "import random\n", + "random_index=random.randint(0,len(train_dataset)-1)\n", + "image,label=train_dataset[random_index]\n", + "print(image.shape)" + ], + "metadata": { + "id": "aWXiUq5qLJVA", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "a71012cf-5a7e-4552-ea07-1b6f6582eb92" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "torch.Size([1, 28, 28])\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "import torch.nn as nn\n", + "class neural_net(nn.Module):\n", + " def __init__(self):\n", + " super(neural_net,self).__init__()\n", + " self.fc1=nn.Linear(784,128)\n", + " self.fc2=nn.Linear(128,64)\n", + " self.fc3=nn.Linear(64,10)\n", + "\n", + " def forward(self,x):\n", + " x=x.view(-1,784)\n", + " x=self.fc1(x)\n", + " x=torch.relu(x)\n", + " x=torch.relu(self.fc2(x))\n", + " x=self.fc3(x)\n", + " return x\n", + " def backward(self,loss):\n", + " loss.backward()\n", + "\n", + "import torch.optim as optim\n", + "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n", + "model = neural_net().to(device)\n", + "criterion = nn.CrossEntropyLoss()\n", + "optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)\n", + "\n", + "def train(epochs):\n", + " for i in range(epochs):\n", + " model.train()\n", + " for idx,(data,target) in enumerate(train_loader):\n", + " data,target=data.to(device),target.to(device)\n", + " optimizer.zero_grad()\n", + " output=model(data)\n", + " loss=criterion(output,target)\n", + " model.backward(loss)\n", + " optimizer.step()\n", + " if idx % 500 == 0:\n", + " print(f\"Epoch {i+1}/{epochs}, Batch {idx+1}/{len(train_loader)}, Loss: {loss.item()}\")\n", + " return model\n", + "\n", + "def test_random_sample():\n", + " model.eval()\n", + "\n", + " idx = random.randint(0, len(test_dataset) - 1)\n", + " image, true_label = test_dataset[idx]\n", + "\n", + " plt.imshow(image.squeeze(), cmap='gray')\n", + " plt.title(f\"True Label: {true_label}\")\n", + " plt.axis('off')\n", + " plt.show()\n", + "\n", + " image = image.unsqueeze(0).to(device)\n", + " with torch.no_grad():\n", + " output = model(image)\n", + "\n", + " _, predicted_class = torch.max(output, 1)\n", + "\n", + " probabilities = torch.nn.functional.softmax(output, dim=1)\n", + "\n", + " print(f\"Predicted Label: {predicted_class.item()}\")\n", + " print(\"Class Probabilities:\")\n", + " for i, prob in enumerate(probabilities[0]):\n", + " print(f\"Class {i}: {prob.item()*100:.2f}%\")\n" + ], + "metadata": { + "id": "xATYxnXAF-bg" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "train(epochs=5)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "H2Upo9ubBV0c", + "outputId": "d52a1a25-0e8d-4f6e-df59-30a75c921804" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Epoch 1/5, Batch 1/938, Loss: 2.299408197402954\n", + "Epoch 1/5, Batch 501/938, Loss: 0.09671914577484131\n", + "Epoch 2/5, Batch 1/938, Loss: 0.21627262234687805\n", + "Epoch 2/5, Batch 501/938, Loss: 0.1175546944141388\n", + "Epoch 3/5, Batch 1/938, Loss: 0.11789850145578384\n", + "Epoch 3/5, Batch 501/938, Loss: 0.0226764939725399\n", + "Epoch 4/5, Batch 1/938, Loss: 0.022747565060853958\n", + "Epoch 4/5, Batch 501/938, Loss: 0.021300004795193672\n", + "Epoch 5/5, Batch 1/938, Loss: 0.020878547802567482\n", + "Epoch 5/5, Batch 501/938, Loss: 0.045971985906362534\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "neural_net(\n", + " (fc1): Linear(in_features=784, out_features=128, bias=True)\n", + " (fc2): Linear(in_features=128, out_features=64, bias=True)\n", + " (fc3): Linear(in_features=64, out_features=10, bias=True)\n", + ")" + ] + }, + "metadata": {}, + "execution_count": 14 + } + ] + }, + { + "cell_type": "code", + "source": [ + "test_random_sample()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 636 + }, + "id": "2j9l14kuBedk", + "outputId": "5359a11b-536c-4d61-a2d8-a3636fe557bf" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Predicted Label: 3\n", + "Class Probabilities:\n", + "Class 0: 0.00%\n", + "Class 1: 0.00%\n", + "Class 2: 0.00%\n", + "Class 3: 100.00%\n", + "Class 4: 0.00%\n", + "Class 5: 0.00%\n", + "Class 6: 0.00%\n", + "Class 7: 0.00%\n", + "Class 8: 0.00%\n", + "Class 9: 0.00%\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "**Question 4:**" + ], + "metadata": { + "id": "W-f5WTmxdnuS" + } + }, + { + "cell_type": "code", + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "x=np.arange(0,2*np.pi,0.1)\n", + "y=np.sin(x)\n", + "\n", + "x_val=np.concatenate((np.linspace(-1*np.pi,0,1000),np.linspace(2*np.pi,3*np.pi,1000)))\n", + "y_val=np.sin(x_val)" + ], + "metadata": { + "id": "l3MZVNHiREJJ" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "import torch\n", + "import torch.nn as nn\n", + "import torch.optim as optim\n", + "class SimpleNN(nn.Module):\n", + " def __init__(self,activation_function):\n", + " super(SimpleNN,self).__init__()\n", + " self.activation=activation_function\n", + " self.fc1=nn.Linear(1,64)\n", + " self.fc2=nn.Linear(64,1)\n", + "\n", + " def forward(self,x):\n", + " x=self.fc1(x)\n", + " x=self.activation(x)\n", + " x=self.fc2(x)\n", + " return x\n", + "\n", + "activation_functions={\"ReLU\":nn.ReLU(),\"GeLU\":nn.GELU(),\"SiLU\":nn.SiLU(),\"LeakyReLU\":nn.LeakyReLU(),\"ELU\":nn.ELU()}\n", + "networks = {name: SimpleNN(act_func) for name, act_func in activation_functions.items()}\n", + "\n", + "def train(network,x_train,y_train,x_val,y_val,epochs=1000,lr=0.01):\n", + " criterion=nn.MSELoss()\n", + " optimizer=optim.Adam(network.parameters(),lr=lr)\n", + " training_loss = []\n", + " validation_loss = []\n", + "\n", + " for i in range(epochs):\n", + " network.train()\n", + " optimizer.zero_grad()\n", + " output=network(x_train)\n", + " loss=criterion(output,y_train)\n", + " loss.backward()\n", + " optimizer.step()\n", + " training_loss.append(loss.item())\n", + " network.eval()\n", + " with torch.no_grad():\n", + " output=network(x_val)\n", + " val_loss=criterion(output,y_val)\n", + " validation_loss.append(loss.item())\n", + "\n", + " return training_loss,validation_loss" + ], + "metadata": { + "id": "1dD0ff_pXnxA" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "results={}\n", + "x_train=torch.Tensor(x).unsqueeze(1)\n", + "y_train=torch.Tensor(y).unsqueeze(1)\n", + "x_val=torch.Tensor(x_val).unsqueeze(1)\n", + "y_val=torch.Tensor(y_val).unsqueeze(1)\n", + "for name,network in networks.items():\n", + " training_loss,validation_loss=train(network,x_train,y_train,x_val,y_val,epochs=1000,lr=0.01)\n", + " results[name]={\"Network\":network,\"train_loss\":training_loss,\"val_loss\":validation_loss}\n", + "\n", + "sorted_results = sorted(results.items(), key=lambda x: min(x[1]['val_loss']))\n", + "\n", + "print(\"Order of activation functions by minimum validation loss:\")\n", + "for name, result in sorted_results:\n", + " print(f\"{name}: {min(result['val_loss'])}\")" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "mPisC36qOjvc", + "outputId": "3513c547-4d5b-477b-aa76-c69b1213d0f3" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Order of activation functions by minimum validation loss:\n", + "GeLU: 1.1101047675765585e-05\n", + "SiLU: 4.428025567904115e-05\n", + "LeakyReLU: 0.0001383751950925216\n", + "ELU: 0.0001823971833800897\n", + "ReLU: 0.00030360042001120746\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "fig, axs = plt.subplots(3, 2, figsize=(10, 10))\n", + "axs = axs.ravel()\n", + "\n", + "x_plot = np.linspace(-np.pi, 3 * np.pi, 1000)\n", + "y_true = np.sin(x_plot)\n", + "\n", + "x_train=x_train.reshape(-1)\n", + "y_train=y_train.reshape(-1)\n", + "x_val=x_val.reshape(-1)\n", + "y_val=y_val.reshape(-1)\n", + "for i, (name, result) in enumerate(results.items()):\n", + " network = result['Network']\n", + "\n", + " with torch.no_grad():\n", + " y_pred = network(torch.Tensor(x_plot).unsqueeze(1)).numpy().flatten()\n", + "\n", + " axs[i].plot(x_train, y_train, 'b', label='Training data')\n", + " axs[i].plot(x_val, y_val, 'g', label='Validation data')\n", + " axs[i].plot(x_plot, y_true, 'k--', label='True function',color='yellow')\n", + " axs[i].plot(x_plot, y_pred, 'r', label='Prediction')\n", + " axs[i].set_title(f'{name} Activation')\n", + " axs[i].legend()\n", + " axs[i].set_xlabel('x')\n", + " axs[i].set_ylabel('f(x)')\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "jgcFswHRWOD-", + "outputId": "dfe003b9-5fd6-45f7-d7f2-32455adb9c11" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + ":19: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"k--\" (-> color='k'). The keyword argument will take precedence.\n", + " axs[i].plot(x_plot, y_true, 'k--', label='True function',color='yellow')\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "smoother activation functions like GELU or SiLU can perform better in approximating continuous functions like sine due to their non-linearity therefore, they perform better than ReLU or LeakyReLU and ELU" + ], + "metadata": { + "id": "DpSQIlUkcwHT" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Question 5:**" + ], + "metadata": { + "id": "VEBSDj2vfVY8" + } + }, + { + "cell_type": "code", + "source": [ + "import torch\n", + "import torch.nn as nn\n", + "import torch.optim as optim\n", + "import torchvision\n", + "import torchvision.transforms as transforms\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "class Cifar10CNN(nn.Module):\n", + " def __init__(self, use_batchnorm=False):\n", + " super(Cifar10CNN, self).__init__()\n", + " self.use_batchnorm = use_batchnorm\n", + " self.conv1 = nn.Conv2d(3,16,3,padding=1)\n", + " self.conv2 = nn.Conv2d(16,32,3,padding=1)\n", + "\n", + " if use_batchnorm:\n", + " self.bn1 = nn.BatchNorm2d(16)\n", + " self.bn2 = nn.BatchNorm2d(32)\n", + "\n", + " self.fc = nn.Linear(32*8*8,10)\n", + "\n", + " def forward(self,x):\n", + " x = self.conv1(x)\n", + " if self.use_batchnorm:\n", + " x = self.bn1(x)\n", + " x = nn.functional.relu(x)\n", + " x = nn.functional.max_pool2d(x,2)\n", + " x = self.conv2(x)\n", + " if self.use_batchnorm:\n", + " x = self.bn2(x)\n", + " x = nn.functional.relu(x)\n", + " x = nn.functional.max_pool2d(x, 2)\n", + " x = x.view(-1,32*8*8)\n", + " x = self.fc(x)\n", + " return x\n", + "\n", + "device=torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n", + "\n", + "transform=transforms.Compose([\n", + " transforms.ToTensor(),\n", + " transforms.Normalize((0.5,0.5,0.5),(0.5,0.5,0.5))\n", + "])\n", + "\n", + "trainset = torchvision.datasets.CIFAR10(root='./data', train=True, download=True, transform=transform)\n", + "trainloader = torch.utils.data.DataLoader(trainset, batch_size=64, shuffle=True)\n", + "\n", + "def train_model(model, epochs=5, lr=0.001, momentum=0.9):\n", + " criterion = nn.CrossEntropyLoss()\n", + " optimizer = optim.SGD(model.parameters(), lr=lr, momentum=momentum)\n", + "\n", + " model.to(device)\n", + "\n", + " for epoch in range(epochs):\n", + " running_loss = 0.0\n", + " for i, data in enumerate(trainloader, 0):\n", + " inputs, labels = data\n", + " inputs, labels = inputs.to(device), labels.to(device)\n", + "\n", + " optimizer.zero_grad()\n", + " outputs = model(inputs)\n", + " loss = criterion(outputs, labels)\n", + " loss.backward()\n", + " optimizer.step()\n", + "\n", + " running_loss += loss.item()\n", + " if i % 200 == 199:\n", + " print(f'[{epoch + 1}, {i + 1:5d}] loss: {running_loss / 200:.3f}')\n", + " running_loss = 0.0\n", + "\n", + " print('Finished Training')\n", + "\n", + "model_without_bn = Cifar10CNN(use_batchnorm=False)\n", + "train_model(model_without_bn)\n", + "model_with_bn = Cifar10CNN(use_batchnorm=True)\n", + "train_model(model_with_bn)" + ], + "metadata": { + "id": "gIC8Q-TMcJQ-", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "7e789eff-7c60-4981-d10b-59fc3cca244c" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Downloading https://www.cs.toronto.edu/~kriz/cifar-10-python.tar.gz to ./data/cifar-10-python.tar.gz\n" + ] + }, + { + "output_type": "stream", + "name": "stderr", + "text": [ + "100%|██████████| 170498071/170498071 [00:01<00:00, 94852669.76it/s] \n" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Extracting ./data/cifar-10-python.tar.gz to ./data\n", + "[1, 200] loss: 2.243\n", + "[1, 400] loss: 2.037\n", + "[1, 600] loss: 1.873\n", + "[2, 200] loss: 1.731\n", + "[2, 400] loss: 1.685\n", + "[2, 600] loss: 1.601\n", + "[3, 200] loss: 1.524\n", + "[3, 400] loss: 1.490\n", + "[3, 600] loss: 1.468\n", + "[4, 200] loss: 1.405\n", + "[4, 400] loss: 1.365\n", + "[4, 600] loss: 1.355\n", + "[5, 200] loss: 1.309\n", + "[5, 400] loss: 1.293\n", + "[5, 600] loss: 1.267\n", + "Finished Training\n", + "[1, 200] loss: 1.731\n", + "[1, 400] loss: 1.440\n", + "[1, 600] loss: 1.323\n", + "[2, 200] loss: 1.198\n", + "[2, 400] loss: 1.149\n", + "[2, 600] loss: 1.134\n", + "[3, 200] loss: 1.053\n", + "[3, 400] loss: 1.041\n", + "[3, 600] loss: 1.024\n", + "[4, 200] loss: 0.970\n", + "[4, 400] loss: 0.958\n", + "[4, 600] loss: 0.983\n", + "[5, 200] loss: 0.923\n", + "[5, 400] loss: 0.920\n", + "[5, 600] loss: 0.918\n", + "Finished Training\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "def get_activation_maps(model, input_image):\n", + " model.eval()\n", + " x = input_image.unsqueeze(0).to(device)\n", + "\n", + " conv1_out = model.conv1(x)\n", + " if model.use_batchnorm:\n", + " conv1_out = model.bn1(conv1_out)\n", + " conv1_act = nn.functional.relu(conv1_out)\n", + " conv2_out = model.conv2(nn.functional.max_pool2d(conv1_act, 2))\n", + " if model.use_batchnorm:\n", + " conv2_out = model.bn2(conv2_out)\n", + " conv2_act = nn.functional.relu(conv2_out)\n", + "\n", + " return conv1_out, conv1_act, conv2_out, conv2_act\n", + "\n", + "def plot_activations(conv1_out, conv1_act, conv2_out, conv2_act, use_batchnorm=False):\n", + " fig, axs = plt.subplots(2, 4, figsize=(20, 10))\n", + "\n", + " axs[0, 0].imshow(conv1_out[0, 0].cpu().detach().numpy())\n", + " axs[0, 0].set_title('Conv1 Output')\n", + " axs[0, 1].hist(conv1_out.cpu().detach().numpy().flatten(), bins=50)\n", + " axs[0, 1].set_title('Conv1 Output Distribution')\n", + "\n", + " axs[0, 2].imshow(conv1_act[0, 0].cpu().detach().numpy())\n", + " axs[0, 2].set_title('Conv1 Activation')\n", + " axs[0, 3].hist(conv1_act.cpu().detach().numpy().flatten(), bins=50)\n", + " axs[0, 3].set_title('Conv1 Activation Distribution')\n", + "\n", + " axs[1, 0].imshow(conv2_out[0, 0].cpu().detach().numpy())\n", + " axs[1, 0].set_title('Conv2 Output')\n", + " axs[1, 1].hist(conv2_out.cpu().detach().numpy().flatten(), bins=50)\n", + " axs[1, 1].set_title('Conv2 Output Distribution')\n", + "\n", + " axs[1, 2].imshow(conv2_act[0, 0].cpu().detach().numpy())\n", + " axs[1, 2].set_title('Conv2 Activation')\n", + " axs[1, 3].hist(conv2_act.cpu().detach().numpy().flatten(), bins=50)\n", + " axs[1, 3].set_title('Conv2 Activation Distribution')\n", + "\n", + " plt.tight_layout()\n", + " plt.suptitle(f'Activations {\"with\" if use_batchnorm else \"without\"} BatchNorm', fontsize=16)\n", + " plt.show()\n", + "\n", + "dataiter = iter(trainloader)\n", + "images, _ = next(dataiter)\n", + "input_image = images[2]\n", + "\n", + "conv1_out, conv1_act, conv2_out, conv2_act = get_activation_maps(model_without_bn, input_image)\n", + "plot_activations(conv1_out, conv1_act, conv2_out, conv2_act, use_batchnorm=False)\n", + "\n", + "conv1_out, conv1_act, conv2_out, conv2_act = get_activation_maps(model_with_bn, input_image)\n", + "plot_activations(conv1_out, conv1_act, conv2_out, conv2_act, use_batchnorm=True)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "bzt74rHU3qmt", + "outputId": "bb7ee2cc-fb5c-4595-d01b-297b6b6441b6" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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+ }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "BatchNorm works beacuse it make the network less sensitive to the size of the weights of the previous layer, and since it can hande larger weights the learning rate can be increased too, hence speeding up the training. Also the activation patterns are more pronounced as observable." + ], + "metadata": { + "id": "NVdEa-Pa6mN6" + } + } + ] +} \ No newline at end of file