Weekly Schedule
This schedule is provisional and may be adjusted to match the class’s pace.
| Week | Lectures | Lecture topics | Casella & Berger |
|---|---|---|---|
| 0 | Sep. 24 | Course overview; use of AI; probability and uncertainty; experiments, outcomes, and sample spaces | §1.1 |
| 1 | Sep. 29, Oct. 1 | Set theory; events and set operations; partitions; $\sigma$-algebras; probability axioms; the calculus of probabilities | §§1.1–1.2.2 |
| 2 | Oct. 6, 8 | Counting and enumerating outcomes; conditional probability and Bayes’ rule; independence | §§1.2.3–1.3 |
| 3 | Oct. 13, 15 | Random variables; cumulative distribution functions; probability mass and density functions | §§1.4–1.6 |
| 4 | Oct. 20, 22 | Distributions of functions of a random variable (cdf and change-of-variable methods); expected values | §§2.1–2.2 |
| 5 | Oct. 27, 29 | Moments and moment generating functions; differentiating under an integral sign | §§2.3–2.4 |
| 6 | Nov. 3, Nov. 5 (midterm) | Midterm review; midterm examination | Chapters 1–2 |
| 7 | Nov. 10, 12 | Discrete families (uniform, hypergeometric, binomial, Poisson, negative binomial/geometric); continuous families (uniform, gamma/exponential, $\chi^2$, normal, beta, Cauchy) | §§3.1–3.3 |
| 8 | Nov. 17, 19 | Exponential families; location and scale families; inequalities and identities. Multiple random variables: joint and marginal distributions | §§3.4–3.6, 4.1 |
| 9 | Nov. 24 (no class Nov. 26) | Conditional distributions and independence; bivariate transformations | §§4.2–4.3 |
| 10 | Dec. 1, 3 | Hierarchical models and mixtures; covariance and correlation; multivariate distributions (multinomial, bivariate normal); inequalities; final review | §§4.4–4.7 |
| Finals | Dec. 10 (final) | Comprehensive final examination | Chapters 1–4 |