Lectures 22-26 are from the Fall 2009 version of the course.
Lecture notes files.
| 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) |
