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 | |