| Date | Chapter | Description | |
|---|---|---|---|
| Sep 1 | 1.1 | Introduction, simulations | |
| Sep 3 | 1.1 | More simulations, distribution functions | |
| Sep 6 | Labor Day! (no class) | ||
| Sep 8 | 1.2 | Discrete distributions -> probability | |
| Sep 10 | 2.1 | Simulating continuous distributions | |
| Sep 13 | 2.1, 2.2 | Bertrand's paradox, density functions | |
| Sep 15 | 2.2 | Density function examples | |
| Sep 17 | 2.2 | Cumulative distribution functions, exponential distribution | |
| Sep 20 | 2.2, 3.1 | Infinite coin flips, permutations | |
| Sep 22 | 3.2 | Combinations, the binomial theorem | |
| Sep 24 | 3.2 | Bernoulli processes, binomial random variables | |
| Sep 27 | 3.2 | Hypothesis testing in Bernoulli processes | |
| Sep 29 | 3.2 | Inclusion-exclusion, derangements | |
| Oct 1 | 3.2, 3.3 | Derangements, riffle shuffle model | |
| Oct 4 | 3.3 | Riffle shuffles: Rising sequences and interleavings | |
| Oct 6 | Exam 1 | ||
| Oct 8 | 3.3 | Riffle shuffles: Variation distance | |
| Oct 11 | 4.1 | Conditional probability, Monty Hall | |
| Oct 13 | 4.1 | Independence of events | |
| Oct 15 | Fall Break! (no class) | ||
| Oct 18 | 4.1 | Random variables, extended | |
| Oct 20 | 4.1 | Joint distributions and independence | |
| Oct 22 | 4.1 | Bayes' Theorem | |
| Oct 25 | 4.2 | Continuous conditional probability | |
| Oct 27 | 4.2 | Independence of continuous R.V.'s | |
| Oct 29 | 5.1 | Geometric, negative biomial, Poisson distributions | |
| Nov 1 | 5.1, 5.2 | More Poisson distribution | |
| Nov 3 | 5.2 | Functions of R.V.'s, how to simulate continuous R.V.'s | |
| Nov 5 | 5.2 | Normal random variables, and the idea of Central Limit Theorems | |
| Nov 8 | 6.1 | Expected value | |
| Nov 10 | 6.1 | Linearity of expectation applications | |
| Nov 12 | Exam 2 | ||
| Nov 15 | 6.1, 6.2 | Conditional expectation; Variance | |
| Nov 17 | 6.2 | Variance -> "extra weak LLN" | |
| Nov 19 | 6.2, 6.3 | Variance examples, Continuous expectation and variance | |
| Nov 22 | 6.3 | Expectation and variance of exponential and normal RVs | |
| Nov 24 | Thanksgiving! (no class) | ||
| Nov 26 | Thanksgiving! (no class) | ||
| Nov 29 | 7.1 | Discrete convolutions | |
| Dec 1 | 7.2 | Continuous convolutions | |
| Dec 3 | 8.1 - 8.2 | Chebyshev Lemma and Weak LLN | |
| Dec 6 | 8.2, 9 | LLN applications, CLT statement | |
| Dec 8 | 9.1 | Proof of binomial CLT | |
| Dec 10 | 9.1 | Ideas towards general CLT; Applications of CLT | |
| Dec 20 | Final exam (6:00 pm - 8:00 pm) | ||