### 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) |