Lectures 22-26 are from the Fall 2009 version of the course.
| LEC # | TOPICS | LECTURE NOTES |
|---|---|---|
| 1 | Probabilistic models and probability measures | (PDF) |
| 2 | Two fundamental probabilistic models | (PDF) |
| 3 | Conditioning and independence | (PDF) |
| 4 | Counting | (PDF) |
| 5 | Random variables | (PDF) |
| 6 | Discrete random variables and their expectations | (PDF) |
| 7 | Discrete random variables and their expectations (cont.) | (PDF) |
| 8 | Continuous random variables | (PDF) |
| 9 | Continuous random variables (cont.) | (PDF) |
| 10 | Derived distributions | (PDF) |
| 11 | Abstract integration | (PDF) |
| 12 | Abstract integration (cont.) | (PDF) |
| 13 | Product measure and Fubini's theorem | (PDF) |
| 14 | Moment generating functions | (PDF) |
| 15 | Multivariate normal distributions | (PDF) |
| 16 | Multivariate normal distributions: characteristic functions | (PDF) |
| 17 | Convergence of random variables | (PDF) |
| 18 | Laws of large numbers | (PDF) |
| 19 | Laws of large numbers (cont.) | (PDF) |
| 20 | The Bernoulli and Poisson processes | (PDF) |
| 21 | The Poisson process | (PDF) |
| 22 | Markov chains | (PDF) |
| 23 | Markov chains II: mean recurrence times | (PDF) |
| 24 | Markov chains III: periodicity, mixing, absorption | (PDF) |
| 25 | Infinite Markov chains, continuous time Markov chains | (PDF) |
| 26 | Birth-death processes | (PDF) |