This is a schedule for what I have covered and what I plan to cover in class each day. This section will be updated regularly during the semester.
| Date |
Topic |
Homework |
Due |
| Mon, August 27 | Introduction. The sample space. | Chapter 1.8: 4,16; | Sep 5 |
| Wed, August 29 | Probabilities. | Chapter 2.10: 1,3,4,5,11,15. | Sep 5 |
| Fri, August 31 | Combinatorial Analysis | ||
| Mon, September 3 | Labor day; No classes | ||
| Wed, September 5 | Combinatorial Analysis, Binomial series | Chapter 2.10: 17, 19, 27, 32, 38 | Sep 12 |
| Fri, September 7 | Hypergeometric distribution | Chapter 2.11: 3,5,6 | Sep 12 |
| Mon, September 10 | Waiting times | Chapter 2.10: 35,36 | Sep 19 |
| Wed, September 12 | Random walks | Chapter 3.10: 1,2,3,4 | Sep 19 |
| Fri, September 14 | Random walks - the reflection principle | Part of homework 3 | Sep 19 |
| Mon, September 17 | Random walks - first and last return probabilities | Chapter 3.10: 6,7,11,12 | Sep 26 |
| Wed, September 19 | Random walks - steps on the positive side, maxima | ||
| Fri, September 21 | Combination of events, Conditional probability | Chapter 4.6: 3,8,12,15 | Sep 26 |
| Mon, September 24 | Stratified populations, Independence | Chapter 5.8: 2,6,7,15,16, | Oct 5 |
| Wed, September 26 | Binomial distribution, law of large numbers | Chapter 6.10: 3,5,6 | Oct 5 |
| Fri, September 28 | Poisson distribution, Poisson process | ||
| Mon, October 1 | Midterm 1 | ||
| Wed, October 3 | Normal distribution | Chapter 6.10: 11,12,17,20,23,27,41 | Oct 17 |
| Fri, October 5 | Expectation, variance, standard deviation | Part of homework 6 | Oct 17 |
| Mon, October 8 | More on the normal distribution | ||
| Wed, October 10 | Midterm exam overview | ||
| Fri, October 12 | DeMoivre-Laplace limit theorem | ||
| Mon, October 15 | Examples; Normal approximation to the poisson distribution | ||
| Wed, October 17 | Large deviations | Chapter 7.7: 2,4,5,7,9,12,13,14 | Oct 26 |
| Fri, October 19 | Mid-Semester Break; No Classes | ||
| Mon, October 22 | Infinite Bernoulli trials | ||
| Wed, October 24 | Borel-Cantelli Lemmas | Part of homework 8 | Nov 2 |
| Fri, October 26 | Strong law of large numbers | Chapter 8: 1,2,3,4,5,6 | Nov 2 |
| Mon, October 29 | Conditional distribution and conditional expectation | Extra credit problem (Blackboard) | Nov 9 |
| Wed, October 31 | Joint distribution | Part of homework 9 | Nov 9 |
| Fri, November 2 | Covariance | Chapter 9: 2,8,9,10,21,34 | Nov 9 |
| Mon, November 5 | Midterm 2 | ||
| Wed, November 7 | The weak law of large numbers | Chapter 10:1,2ab,6,8 | Nov 16 |
| Fri, November 9 | Absolutely continuous random variables | Part of homework 10 | Nov 16 |
| Mon, November 12 | Joint density, marginals, conditional expectation | ||
| Wed, November 14 | The partition theorem | ||
| Fri, November 16 | Transformed random variables | Homework 11 | Nov 30 |
| Mon, November 19 | The multivariate normal distribution | ||
| Wed, November 21 | Thanksgiving Holiday; No Classes | ||
| Fri, November 23 | Thanksgiving Holiday; No Classes | ||
| Mon, November 26 | Generating functions | ||
| Wed, November 28 | Characteristic functions | ||
| Fri, November 30 | Proof of the Central Limit Theorem. Brownian Motion | Homework 12 | Dec 7 |
| Mon, December 3 | Brownian Motion | ||
| Wed, December 5 | Brownian Bridge | ||
| Fri, December 7 | Construction of a Poisson process |