Lecture Notes

Lectures 22-26 are from the Fall 2009 version of the course.

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)