Date | Topic | Notes |
---|---|---|
Tu, Sept 4 | Introduction, sample spaces, probability axioms | Read chapter 1 in the book. Due for Th 9/6: Problems 1.4.2, 1.4.4, 1.4.6, 1.5.2, 1.5.4, 1.5.6, 1.5.10, 1.5.12 from the book. Lecture notes for chapter one here (pdf). |
Th, Sept 6 | Combinatorics, Stirling's approximation; conditional probability | Read chapter 2.1-2.3 in the book. Due T 9/11: Problems 1.6.2, 1.6.6, 1.6.8, 1.7.2, 1.7.4, 1.7.6, 1.7.8, 1.7.10, 1.8.2, 1.8.8, 1.8.14, 1.9.4, 1.9.8. |
Tu, Sept 11 | More on conditional probabilities, Bayes rule | Due Th 9/13: Problems 1.12.2, 1.12.10, 2.1.2, 2.1.6, 2.1.8, 2.2.2, 2.2.4, 2.2.6, 2.2.10, 2.3.8, 2.3.10, 2.3.20. Lecture notes for chapter two here (pdf). |
Th, Sept 13 | Independent events. Random variables and distributions; pmf's, pdf's, and cdf's | Read chapter 3 in the book. Due Tu 9/18: Problems 2.2.12, 2.2.14, 2.3.12, 2.3.18, 3.1.2, 3.1.4, 3.1.6. |
Tu, Sept 18 | Multivariate distributions; functions of a random variable; convolution | Due Th 9/20: Problems 3.1.8, 3.2.2, 3.2.4, 3.2.8, 3.2.10, 3.3.2, 3.3.14, 3.4.2, 3.4.4. Lecture notes for chapter three here (pdf). |
Th, Sept 20 | Expectations, variance | Read chapter 4 in the book. Due Tu 9/25: Problems 3.8.2, 3.8.6, 3.8.8, 3.9.2, 3.9.4, 3.9.8, 3.9.16, 3.10.20. Lecture notes for chapter four here. |
Tu, Sept 25 | Moment-generating functions; Covariance and correlation; sample means | Due Th 9/27: Problems 4.1.2, 4.1.12, 4.2.2, 4.2.8, 4.2.10, 4.3.2, 4.3.4, 4.3.6, 4.4.2, 4.4.4, 4.4.10. |
Th, Sept 27 | Inequalities: Markov, Chebyshev, Chernoff, and Jensen; law of large numbers; special discrete distributions | Due for Tu 10/2: Problems 3.5.2, 3.5.4, 3.5.6, 3.6.2, 3.6.4, 3.6.10, 3.7.2, 3.7.8. Lecture notes for inequalities here. |
Tu, Oct 2 | Special continuous distributions; order statistics | Read chapter 5 in the book. Due Th 10/4: Problems 4.5.2, 4.5.6, 4.5.12, 4.6.4, 4.6.8, 4.6.10, 4.7.2, 4.7.6, 4.7.12, 4.8.2, 4.8.8, 4.8.12. Lecture notes for chapter five here. |
Th, Oct 4 | Central limit theorem; convergence in distribution | Due Tu 10/9: Problems 5.2.4, 5.2.6, 5.2.8, 5.3.2, 5.3.6, 5.3.8, 5.4.2, 5.4.8, 5.4.14, 5.5.2, 5.5.6. Notes on CLT here. |
Tu, Oct 9 | Basic simulation theory: Monte Carlo integration, importance sampling | Read chapter 11.1-11.3 in the book. Due Th 10/11: Problems 5.6.2(a)-(d), 5.6.6, 5.6.12, 5.6.14, 5.6.18, 5.7.2, 5.7.4, 5.7.6, 5.7.10. |
Th, Oct 11 | Decision theory | Read chapter 6 in the book, and reread section 4.9. Due Tu 10/16: Problems 5.8.2, 5.8.6, 5.9.6, 5.9.16, 5.9.18, 5.9.22, 5.10.2, 5.10.8, 5.11.4, 11.2.2, 11.2.4. Notes on decision theory here. |
Tu, Oct 16 | Introduction to estimation theory; Bayes estimation; maximum likelihood | Due Th 10/18: Problems 4.9.4, 4.9.6, 4.9.8, 6.2.4, 6.2.6, 6.2.10, 6.3.6, 6.3.10, 6.3.12. Notes on estimation theory here. |
Th, Oct 18 | Midterm review | No HW Due Th 10/18: midterm (covers material in chapters 1-5 and 11). |
Tu, Oct 23 | Midterm exam | No HW due Th 10/25. |
Th, Oct 25 | Bias and variance; more on maximum likelihood | Due Tu 10/30: Problems 6.3.8, 6.4.2, 6.4.4, 6.4.8, 6.5.2, 6.5.6, 6.5.10, 6.6.2, 6.6.4 |
Tu, Oct 30 | Sufficiency; exponential families | Read chapter 7 in the book. Due Th 11/1: Problems 6.6.6, 6.6.12, 6.7.2, 6.7.6, 6.8.4, 6.8.14, 6.9.2, 6.9.8, 6.9.14. |
Th, Nov 1 | More on exponential families: conjugate priors, method of moments. Asymptotic ideas: consistency, asymptotic efficiency | Due Th 11/8: Problems 7.1.2, 7.1.4, 7.1.6, 7.1.8, 7.2.2, 7.2.4, 7.2.10, 7.3.6a, 7.3.8. |
Tu, Nov 6 | No class - University holiday | Remember to vote... |
Th, Nov 8 | Consistency of the MLE; Kullback-Leibler divergence. Asymptotic normality of the MLE; Fisher information; Cramer-Rao bound | Due Tu 11/13: Problems 7.5.2, 7.5.6, 7.5.10, 7.6.2, 7.7.2, 7.7.4, 7.7.6 |
Tu, Nov 13 | Simple hypothesis testing; likelihood ratio tests; Neyman-Pearson lemma | Read chapter 8 in the book. Notes on hypothesis testing here. Due Th 11/15: Problems 7.7.8, 7.7.14, 7.8.2, 7.8.4, 7.8.8, 7.9.6, 7.9.16. |
Th, Nov 15 | Hypothesis testing with compound alternates; uniformly most powerful tests | Due Tu 11/20: Problems 8.1.2, 8.1.4, 8.1.8, 8.1.14, 8.2.4, 8.2.7, 8.3.2, 8.3.6, 8.3.12. |
Tu, Nov 20 | Testing with compound null hypotheses; t-tests, F-tests | Due Tu 11/27: Problems 8.4.4, 8.4.6, 8.4.12, 8.5.2, 8.5.6, 8.5.8, 8.6.2, 8.6.8, 8.7.2, 8.7.8. Read chapter 9 in the book. |
Th, Nov 22 | No class | Happy thanksgiving. |
Tu, Nov 27 | Chi-square tests for goodness of fit, homogeneity, and independence | Due Th 11/29: Problems 9.1.4, 9.1.6, 9.1.8, 9.2.2, 9.2.4, 9.3.4, 9.3.6, 9.4.4. |
Th, Nov 29 | Nonparametrics: Kolmogorov-Smirnov / sign and rank tests. Basics of linear regression. | Due Tu 12/4: Problems 9.6.3, 9.6.4, 9.8.2, 9.8.12, 9.9.4, 9.9.6, 9.9.14 |
Tu, Dec 4 | The EM algorithm; fitting mixture models | Due Th 12/6: E-mail me questions for the review. |
Th, Dec 6 | Review session - last class. | E-mail me questions. See here for some extra course notes to help study. |
Tu, Dec 18 | Final exam | Note change in time: 7:10-10:00 pm (usual place). |