Schedule (subject to change!)
Warning: Dates in the future (in particular, assignment release and due dates) will sometimes change to adjust to the pace I cover the material.
Note: files for assignments under Files.
Note: Abbreviations:
- Gu stands for A. Gut, Probability: A graduate course, 2nd edition. Springer. Note: the pdf of this textbook is freely available via UBC Library.
- G+S stands for G.R. Grimmett and D.R. Stirzaker, Probability and Random Processes, 3rd edition (the textbook),
- Du stands for R. Durrett, Probability: Theory and Examples, 4th edition, Cambridge U. Press (2010). Available online: URL.
- Bi stands for P. Billingsley, Probability and Measure, 3rd edition, John Wiley and Sons, New York (1995).
| Meeting | Notes | Topics | Readings | Homework (out) | Homework (due) |
| Sep 5 | Overview, motivation. | G+S 1.*; Du 1.1, 1.2, 1.3; Gu p. 1-6 | |||
| Sep 10 | Probability spaces | Exercise 1 | |||
| Sep 12 | Probability spaces, continued | ||||
| Sep 17 | Random variables, distribution, cdf. | G+S 5.6; Du 1.4, 1.5; Bi 15; Gu p. 7-13 | Exercise 1 | ||
| Sep 19 | Distribution, cdf. | G+S 7.3; Du 1.6; Gu p. 25-32 | Exercise 2 | ||
| Sep 24 | Expectation: basics | Assignment 1 | Exercise 2 | ||
| Sep 26 | More on expectations. | Du 1.7; Bi 18; Gu p. 45-58 | |||
| Oct 1 | Limits and expectations. | ||||
| Oct 3 | Independence. Intro to multivariate models. | Gu p. 60-67 | Exercise 3 | Assignment 1 | |
| Oct 8 | Thanksgiving! | No class | Gu p. 68-73 | ||
| Oct 10 | Borel-Cantelli, random walks. | G+S 7.2, 7.4, 7.5; Du 2.2; Bi 5; Gu p. 96-104 | Exercise 3 | ||
| Oct 15 | WLLN, convergence in probability and almost sure. | G+S 5.1, 5.4; Du 3.3; Gu p. 201-213 | |||
| Oct 17 | MIDTERM | MIDTERM (regular lecture time and location) | |||
| Oct 22 | Generating functions, if time permits, branching processes | G+S 5.7, 5.10; Du 3.4; Gu p. 157-164 | Exercise 4 | ||
| Oct 24 | Characteristic functions, CLTs | G+S 4.12; Du 3.6 | |||
| Oct 29 | Characteristic functions, CLTs, continued | Exercise 4 | |||
| Oct 31 | Poisson processes | G+S 6.13, Gu p.459-464 | |||
| Nov 5 | Poisson processes, continued | Assignment 2 | |||
| Nov 7 | Conditioning | G+S 4.5; Du 5.1; B 32 | |||
| Nov 12 | Remembrance day | No class | |||
| Nov 14 | Guest lecture on martingales | Assignment 2 | |||
| Nov 19 | Conditioning, continued | ||||
| Nov 21 | Markov chains 1: Examples, classification of states, hitting probabilities | G+S 6.1, 6.2, 6.3; Du 5.3 | |||
| Nov 23 | Assignment 3 | ||||
| Nov 26 | Markov chains 2: LLN/CLT, stationary measures | G+S 4.12, 6.4; Du 5.4, 5.5 | |||
| Nov 28 | EXAM | ||||
| Dec 5 | Assignment 3 |