| Prof: | Robert L. Wolpert | wolpert@stat.duke.edu (684-3275) | |
| OH: | Mon & Wed 2:00-3:00pm | Old Chemistry 211c | |
| Class: | Tue & Thu 12:40-1:55pm | Old Chemistry 025 | |
| Texts: | Patrick Billingsley, | Probability and Measure (3rd edn) | |
| Grimmett & Stirzaker, | Probability and Random Processes (2nd edn) | ||
| Refs: | Leo Breiman, | Probability | |
| Kai Lai Chung, | A Course in Probability Theory (2nd edn) | ||
| David Williams, | Probability with Martingales | ||
| A.N. Shiryaev, | Probability (2nd edn) |
Mathematical topics from real analysis, including parts of measure theory, Fourier and functional analysis, are introduced as needed to support a deep understanding of probability and its applications. Topics of later interest in statistics (e.g., regular conditional density functions) are given special attention, while those of lesser statistical interest (e.g., extreme value theorems) may be omitted.
Some problems and projects may require computation; you are free to use whatever environmnent you're most comfortable with. Most people find S-Plus (some notes are available) or Matlab (a primer is available) easier to use than compiled languages like f77, c, or c++. Homework problems are of the form text/chapter/problem with GS or PB for the texts, Grimett & Stirzaker or Patrick Billingsley. Not all of them will be graded, but they should be turned in for comment; Tuesday classes will begin with a class solution of two of the preceeding week's problems. Some weeks will have lecture notes added (click on the "Week" column if it's blue or green). This is syllabus is tentative, correct as of Oct 20 1998, and will almost surely be superceded.
| Week | Topic | Homework Problems | |
|---|---|---|---|
| I. Foundations of Probability | |||
| Sep 1 | Events, Probabilities, and Independence | GS1/1,3,4,7,14,16 | |
| Sep 8 | Random Variables and Distributions | GS2/1,2,3,5,7,14 | |
| Sep 15 | Discrete Random Variables | GS3/4,6,12,14,16 | |
| Sep 22 | Continuous & Singular (e.g. Cantor) RV's | GS4/7,8,9,18,26,27 | |
| Sep 29 | Transforms of Distributions | GS5/2,24,26,27,34-37 | |
| Oct 6 | Fourier Transforms and Inversion | ||
| --- Fall Break (Oct 9-13) --- | |||
| II. Convergence of Random Variables & Distributions | |||
| Oct 15 | Central Limit Theorem | ||
| Oct 20 | Convergence of Random Variables I | GS7/1,4,9,10,12 | |
| Oct 27 | Convergence of Random Variables II | GS7/2i,3,6,16,17,20 | |
| Nov 3 | Conditional Probability & Expectation | Midterm Exam (Due Nov 10) | |
| III. Conditional Probability & Expectation | |||
| Nov 10 | Martingales: Intro & Stopping Times | ||
| Nov 17 | Martingales: Maxima & Limits | GS12.1/13,14,16,18; 12.5/26 | |
| Nov 24 | Sequential Statistical Tests | ||
| --- Thanksgiving Break (Nov 25-28) --- | |||
| Dec 1 | Brownian Motion | ||
| Dec 4 | Graduate Classes End | ||
| Dec 18 | Scheduled Final Examination (9am-12n). | ||