Lectures

Tuesdays & Thursdays, 2:30pm - 3:50pm, 85 Waterman Street, room 130.

Primary readings below refer to sections in the course textbook, Introduction to Probability (second edition) by Bertsekas and Tsitsiklis. For material in the first half of the course, Pitman's Probability is recommended as a secondary reference.


# Date Topics Primary Reading Materials
0 January 28 Course Overview 1.0 slides
1 February 2 Sets and Events, Counting 1.1-1.2, 1.6 slides
2 February 4 Conditioning, Bayes' Rule 1.3-1.4 slides
3 February 9 Conditioning, Independence 1.4-1.5 slides
4 February 11 Independence, Classification, Discrete Random Variables 1.4-1.5, 2.1 slides
5 February 16 Functions of Random Variables, Expectations 2.2-2.4 slides
6 February 18 Multiple Random Variables, Independence 2.5-2.7 slides
- February 23 HOLIDAY! NO CLASS!

7 February 25 Conditional Expectation, Variance 2.4, 2.6 slides
8 March 1 Cumulative Distributions 3.2 slides
9 March 3 Continuous Probability Densities, Gaussian Distributions 3.1-3.3 slides
10 March 8 Continuous Conditioning, Bayes' Rule 3.4-3.6 slides
11 March 10 Conditional Densities, Derived Distributions 4.1, 4.5 slides
12 March 15 Derived Distributions, Sums of Random Variables 4.1, 4.3 slides
- March 17 MIDTERM EXAM (85 Waterman, room 130)
13 March 22 Covariance, Bivariate Normal Distributions Supplement, 4.2 slides
14 March 24 Multivariate Normals, Linear Regression, Rare Events Supplement, 9.2, 5.1 slides
- March 29 SPRING BREAK!
- March 31 SPRING BREAK!
15 April 5 Law of Large Numbers, Central Limit Theorem 5.2-5.4 slides
16 April 7 Monte Carlo Methods slides
17 April 12 Markov Chain Foundations 7.1 slides
18 April 14 Markov Chain Equilibria 7.2-7.3 slides
19 April 19 Markov Chain Absorption, Bayesian Hypothesis Tests 7.4, 8.2 slides
20 April 21 Bayesian & Frequentist Hypothesis Tests 8.2, 9.3 slides
21 April 26 Maximum Likelihood Parameter Estimation 9.1 slides
- April 28 NO CLASS!
22 May 3 Bayesian Parameter Estimation 8.1, 8.3 slides
23 May 5 Significance Tests, Confidence Intervals, Review 9.4 slides
- May 20 FINAL EXAM (2:00-5:00pm, Salomon 001)