### Lectures

Tuesdays & Thursdays, 2:30-3:50, in CIT 368

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 | Sep 6 | Course Overview | 1.0 | slides |

1 | Sep 11 | Sets and Events, Counting | 1.1-1.2, 1.6 | slides |

2 | Sep 13 | Conditioning, Bayes' Rule | 1.3-1.4 | slides |

3 | Sep 18 | Conditioning, Independence | 1.4-1.5 | slides |

4 | Sep 20 | Independence, Classification, Discrete Random Variables | 1.4-1.5, 2.1 | slides |

5 | Sep 25 | Functions of Random Variables, Expectations | 2.2-2.4 | slides |

6 | Sep 27 | Multiple Random Variables, Independence | 2.5-2.7 | slides, Naive Bayes notes |

7 | Oct 2 | Conditional Expectation, Variance | 2.4, 2.6 | slides |

8 | Oct 4 | Cumulative Distributions | 3.2 | slides |

9 | Oct 9 | Continuous Probability Densities, Gaussian Distributions | 3.1-3.3 | slides |

10 | Oct 11 | Continuous Conditioning, Bayes' Rule | 3.4-3.6 | slides |

11 | Oct 16 | Conditional Densities, Derived Distributions | 4.1, 4.5 | slides |

12 | Oct 18 | Derived Distributions, Sums of Random Variables | 4.1, 4.3 | slides |

13 | Oct 23 | Covariance, Bivariate Normal Distributions | Supplement, 4.2 | see above slides |

14 | Oct 25 | Multivariate Normals, Linear Regression, Rare Events | Supplement, 9.2, 5.1 | slides |

M | Oct 30 | MIDTERM EXAM | ||

15 | Nov 1 | Law of Large Numbers, Central Limit Theorem | 5.2-5.4 | slides |

16 | Nov 6 | Monte Carlo Methods | slides | |

17 | Nov 8 | Markov Chain Foundations | 7.1 | slides |

18 | Nov 13 | Markov Chain Equilibria | 7.2-7.3 | slides |

19 | Nov 15 | Markov Chain Absorption, Bayesian Hypothesis Tests | 7.4, 8.2 | slides |

20 | Nov 20 | Bayesian & Frequentist Hypothesis Tests | 8.2, 9.3 | slides |

21 | Nov 27 | Maximum Likelihood Parameter Estimation | 9.1 | slides |

22 | Nov 29 | Bayesian Parameter Estimation | 8.1, 8.3 | slides |

23 | Dec 4 | Significance Tests, Confidence Intervals, Review | 9.4 | slides |

F | Dec 17 | FINAL EXAM (9:00-12:00pm, TBA) |