- Course syllabus.
- Online Video Lectures.
- Lecture Notes, solutions to selected problems, and some extra materials.
- Code and Programs.
| 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 |
- 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