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ST 121: Probability and Statistics I

Resources

Lectures:

01. (Sec. 1.1 - 1.4) Introduction, Sample Space, Probability Measure and Counting Methods
02. (Sec. 1.4) Counting Methods
03. (Sec. 1.5) Conditional Probability
04. (Sec. 1.5 - 1.6) Conditional Probability and Independence
05. (Sec. 2.1) Discrete Random Variable
06. (Sec. 2.1) Discrete Random Variable (cont.)
07. (Sec. 2.2) Continuous Random Variable
08. (Sec. 2.2) Continuous Random Variable (cont.)
09. (Sec. 2.3) Functions of Random Variables
10. (Sec. 2.3) Functions of Random Variables (cont.)
11. (Sec. 3.1 - 3.2) Introduction and Discrete Random Vectors
12. (Sec. 3.3) Continuous Random Vectors
13. (Sec. 3.4) Independent Random Vectors
14. (Sec. 3.5) Conditional Distributions
15. (Sec. 3.6.1) Single Function of Jointly Distributed Random Variables
16. (Sec. 3.6.2) p Functions of p Random Variables ( Space Transformation )
17. (Sec. 3.7) Extrema and Order Statistics
18. (Sec. 4.1) The Expected Value of a Random Variable
19. (Sec. 4.1.1 - 4.1.2) Expectations of Functions and Linear Combinations of Random Variable
20. (Sec. 4.2) Variance and Standard Deviation
21. (Sec. 4.3) Covariance and Correlation
22. (Sec. 4.3) Covariance and Correlation (cont.)
23. (Sec. 4.4) Conditional Expectation and Prediction
24. (Sec. 4.5 - 4.6) The Moment-Generating Function and Approximate Methods
25. (Sec. 5.1 - 5.2) The Law of Large Numbers, Convergence in Distribution and CLT
26. (Appendix) Simulation

Assignments

  • Ch1:
    • Solve 2, 4, 7, 12, 21, 23, 34, 35, 39, 42, 45, 46, 53, 54, 64, 68, 70, 71, 72, 76.
    • Write a computer program to calculate the probability of Example C, Section 1.5.
  • Ch2: Solve 1, 2, 3, 4, 6, 8, 9, 13, 14, 16, 21, 23, 28, 30, 33, 34, 37, 38, 40, 44, 46, 47, 51, 53, 54, 58, 59, 61, 67, 69
  • Ch3: Solve 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 19, 23, 31, 42, 48 (very important), 50, 51, 55, 61, 67
  • Ch4: Solve 1, 2, 4, 5, 7, 12, 16, 21, 25, 35, 44, 49(very important), 50, 57, 59, 60, 61, 66, 68, 71, 75, 77, 79, 80, 81, 101, 103
  • Ch5: Solve 3, 5, 10, 12(v. imp.), 17, 18, 19, 25(v. imp.), 30.
  • Simulation: Computer Exercise.

The problem numbers are different in the U.S. edition. The following problems are the mapping of the problems above to the U.S. edition.

  • Ch1: 6, 8, 7, 28, 21, 23, 34, 35, 39, 42, 45, 46, 53, 54, 60, 68, 70, 71, 76, 72.
  • Ch2: 1, 5, 3, 4, 2, 12, 9, 13, 10, 16, 21, 23, 28, 32, 33, 34, 37, 38, 40, 44, 48, 47, 51, 53, 54, 60, 59, 61, 67, 69
  • Ch3: 1, 2, 5, 6, 7, 8, 9, 14, 11, 12, 15, 17, 19, 23, 31, 42, 44, 46, 51, 55, 61, 67
  • Ch4: 1, 4, 2, 5, 7, 16, 12, 21, 25, 35, 44, 49, 50, 57, 59

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