| 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 |