| 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) |