| Week | Topic | Reading | Homework and Exam | Remark |
|---|---|---|---|---|
| Week 1 08/29, 08/31 |
Introduction Algebra of Sets, Probability Function |
Chapter 1.1 Chapter 1.2, 1.3 |
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| Week 2 Labor Day, 09/05,09/7 |
Conditional Prob., Independence, Bayes' Rule Combinatorics, Combinatorial Prob. |
Chapter 1.4 , 1.5 | 1.3.5, 1.3.16, 1.4.31, 1.4.33 |
|
| Week 3 09/10, 09/12 , 09/14 |
Random Variables, cdf, pdf/pmf, |
Chapter 1.6, 1.7 | 1.5.8,1.5.11, 1.6.3, 1.7.9, 1.6.10, 1.7.21 |
HW1 solution |
| Week 4 09/17, 09/19 , 09/21 |
Transformations, Simulations of RV, Expectation, Variance, |
Chapter 1.8, 1.9 | 1.7.18,1.7.24, 1.8.2, 1.8.5, 1.8.7, 1.8.9, |
HW2 solution |
| Week 5 09/24, 09/26 , 09/28 |
Moment Generating Functions, Chebyshev's Inequality, Jensen's inequality, |
Chapter 1.10 | 1.9.1, 1.9.3 1.9.6, 1.9.7 |
HW3 solution |
| Week 6 10/01, 10/03 , 10/05 |
Review of Random Variables & Prob. (for Midterm I), Random vectors and Joint distributions, |
Chapter 2.1 | Midterm I | |
| Week 7 10/08, 10/10 , 10/12 |
Marginal distributions and Transformations, Conditional distributions, |
Chapter 2.2, 2.3 | 1.9.22, 1. 10. 1; 2.1.1, 2.1.2; 2.1.6, 2.1.9; 2.2.1, Find the cdf of Z, where Z=X_1+X_2 and joint pdf of X is given in Example 2.1.2 |
HW4 solution |
| Week 8 10/15, 10/17, Fall Break |
Conditional Expectations, Correlations, |
Chapter 2.4,2.5 | 2.2.3, 2.2.7, 2.2.8, 2.3.2, 2.3.3, 2.3.10 |
HW5 solution |
| Week 9 10/22, 10/24 , 10/26 |
Independence, Linear combinations, |
Chapter 2.8 | 2.2.8, 2.3.11, 2.4.3, 2.4.7 2.5.9, 2.5.11 |
HW6 solution |
| Week 10 10/29, 10/31 , 11/02 |
Bernoulli, Binomial and Multinomial distribution, Negative Binomial and Hypergeometric distribution, |
Chapter 3.1, 3.2 | 2.8.12, 2.8.15, 3.1.3, 3.1.9, |
|
| Week 11 11/05, 11/07 , 11/09 |
Review for Midterm II, Poisson distribution, |
Chapter 3.2 | Midterm II | |
| Week 12 11/12, 11/14 , 11/16 |
Exponential and Gamma distribution, Uniform distribution and Beta distribution |
Chapter 3.3 | 3.1.28 , 3.2.3, 3.2.10, 3.2.13 3.3.6, 3.3.9, 3.3.15 |
HW7 solution |
| Week 13 11/19, Thanksgiving |
Gamma and Beta distribution | Chapter 3.3 | 3.3.23, 3.3.24, 3.3.25, 3.3.26 and Ex 1: Assume that X|Y=y follows Poisson (y) and Y follows Gamma (alpha, beta). Find the distribution of Y|X=x. |
HW8 solution |
| Week 14 11/26, 11/28 , 11/30 |
Conjugate, Normal Distribution, Student t-distribution and Chi-square distribution |
Chapter 3.4, 3.6 | 3.4.1, 3.4.2, 3.4.3 3.4.19(b), 3.4.30, 3.4.31, Ex: Find the Skewness and kurtosis of N(0,1). |
HW9 solution |
| Week 15 12/03, 12/05 , 12/07 |
Distribution of Sample Mean and Sample Variance,
Law of Large Number (LLN), Central Limit Theorem (CLT) |
Chapter 5.1, 5.2 | 3.5.1, 3.5.10, 3.5.16, 3.6.2,3.6.5, 3.6.14(a) |
HW10 solution |
| Final Week 12/17 | Final Exam | Final Exam Solution |
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