| LEC # | TOPICS | KEY DATES |
|---|---|---|
| 1 | Probabilistic models and probability measures | |
| 2 | Two fundamental probabilistic models | Homework 1 due |
| 3 | Conditioning and independence | |
| 4 | Counting | Homework 2 due |
| 5 | Random variables | |
| 6 | Discrete random variables and their expectations | Homework 3 due |
| 7 | Discrete random variables and their expectations (cont.) | |
| 8 | Continuous random variables | |
| 9 | Continuous random variables (cont.) | Homework 4 due |
| 10 | Derived distributions | |
| 11 | Abstract integration | Homework 5 due |
| 12 | Abstract integration (cont.) | Homework 6 due |
| Midterm exam | ||
| 13 | Product measure and Fubini's theorem | |
| 14 | Moment generating functions | |
| 15 | Multivariate normal distributions | Homework 7 due |
| 16 | Multivariate normal distributions: characteristic functions | |
| 17 | Convergence of random variables | |
| 18 | Laws of large numbers | Homework 8 due |
| 19 | Laws of large numbers (cont.) | |
| 20 | The Bernoulli and Poisson processes | Homework 9 due |
| 21 | The Poisson process | |
| 22 | Markov chains | Homework 10 due |
| 23 | Markov chains II: mean recurrence times | |
| 24 | Markov chains III: periodicity, mixing, absorption | Homework 11 due |
| 25 | Infinite Markov chains, continuous time Markov chains | |
| 26 | Birth-death processes |