Lecture Number |
Date |
Sections in Text |
Brief Description |

1 |
3/26 |
1.1 |
Introduction, Examples of Problems, Intuition, Discrete vs. Continuous |

2 |
3/31 |
1.2 |
Fundamental Definitions and Facts about discrete Random Variables |

3 |
4/2 |
3.1 |
Basic Counting Techniques, Examples, Permutations |

4 |
4/3 |
3.1, 3.2 |
More Counting Examples, Binomial Coefficents |

5 |
4/4 |
3.2 |
Poker Hands, Binomial Theorem, Inclusion-Exclusion |

6 |
4/7 |
3.2, 2.1 |
Hat-Check Problem, Stirling's Approximation, Continuous Random Variables |

7 |
4/9 |
2.1, 2.2 |
Bertrand's Paradox, Density Functions, Cumulative Distribution Functions |

8 |
4/11 |
2.2 |
Density Functions and Cumulative Distribution Functions, Examples |

9 |
4/14 |
4.1 |
Discrete Conditional Probability, Independence of Events |

10 |
4/16 |
4.1, 4.2 |
Independence of Random Variables, Continuous Conditional Probability |

11 |
4/18 |
4.2, 5.1 |
Indenpendent Random Variables, Important Distributions |

12 |
4/21 |
5.1, 5.2 |
Poisson Distribution, Normal Random Variables |

13 |
4/23 |
5.2, 6.1 |
Normal Random Variables, Cauchy Density, Expected Value |

14 |
4/25 |
6.1, 6.2 |
Expected Value and Variance of Discrete Random Variables |

15 |
4/28 |
6.2, 6.3 |
Expected Value and Variance of Continuous Random Variables |

16 |
4/30 |
7.1, 7.2 |
Sums of Discrete and Continuous Random Variables |

17 |
5/2 |
8.1, 8.2 |
The Law of Large Numbers |

18 |
5/5 |
11.1 |
Markov Chains |

19 |
5/7 |
11.2 |
Absorbing Markov Chains |

20 |
5/9 |
11.2, 11.3 |
Fundamental Theorems of Absorbing Markov Chains, Motivating Regular and Ergodic Markov Chains |

21 |
5/12 |
11.4 |
Fundamental Theorems of Regular Markov Chains |

22 |
5/14 |
11.5 |
Mean Recurrance Time and Mean First Passage Time |

23 |
5/16 |
9.1 |
Central Limit Theorem for Bernoulli Trials |

24 |
5/19 |
9.2, 9.3, 3.3 |
Central Limit Theorem, Card Shuffling |

25 |
5/21 |
3.3 |
Card Shuffling |

26 |
5/23 |
- |
Introduction to Measure Theory |

17 |
5/28 |
- |
Measure Theory as a Foundation for Proabability Theory |