| Prof: | Robert L. Wolpert | wolpert@stat.duke.edu | OH: Mon 4:15-5pm, 211c Old Chem (684-3275) | ||
| TA: | Zhenglei Gao | zhenglei@stat.duke.edu | OH: Tue, 6:00-9pm, 211a Old Chem (684-8840) | ||
| Aide: | Natesh Pillai | nsp2@stat.duke.edu | OH: Sun, 7-8:30pm, 211a Old Chem (681-9310) | ||
| Class: | Mon/Wed 2:50-4:05pm | ||||
| Text: | Sidney Resnick, | A Probability Path | |||
| Opt'l: | Patrick Billingsley, |
Probability and Measure (3rd edn); | |||
| Week | Topic | Homework | |
|---|---|---|---|
| I. Foundations of Probability | Problems | Due | |
| Jan 09 | No class--- I'm out of the country | ||
| Jan 14,16 | Probability spaces: sets, events, and sigma-fields | hw1 | Jan 23 |
| Jan 23 | Probability spaces: Constructing & extending measures | hw2 | Jan 30 |
| Jan 28-30 | Random variables and their distributions I | hw3 | Feb 06 |
| Feb 04-06 | Random variables and their distributions II | hw4 | Feb 13 |
| Feb 11-13 | Integration & expectation: Lebesgue's MCT \& DCT | hw5 | Feb 20 |
| Feb 18-20 | Independence & zero-one Laws: Fubini's Thm | hw6 | Feb 27 |
| Feb 25-27 | Markov, Chebychev, and Uniform Integrability | hw7 | Mar 03 |
| Mar 03-05 | Review and in-class Midterm (Wed Mar 5) '03, '05, '06, '07 | Results | |
| --- Spring Break (Mar 08-16) --- | |||
| II. Convergence of Random Variables & Distributions | |||
| Mar 17-19 | Convergence concepts: a.s., i.p., Lp, Loo | hw8 | Mar 26 |
| Mar 24-26 | Strong & weak laws of large numbers | hw9 | Apr 02 |
| Mar 31-02 | Convergence in distribution & C.L.T. | hw10 | Apr 09 |
| Apr 07-09 | Stable limit theorem & ID limits (notes) | hw11 | Apr 16 |
| III. Conditional Prob & Expectation | |||
| Apr 14-16 | Radon-Nikodym thm and conditional probability | MGs | |
| Apr 30 | Take-home Final Exam (due 2pm) '03, '04, '05, '06, '07, '08 | Results | |
| May 1 | Histogram of Course Averages | ||
Students are expected to be well-versed in real analysis at the level of W. Rudin's Principles of Mathematical Analysis or M. Reed's Fundamental Ideas of Analysis--- the topology of Rn, convergence in metric spaces (especially uniform convergence of functions on Rn), infinite series, countable and uncountable sets, compactness and convexity, and so forth. Most students who majored in mathematics will be familiar with this material; students with less background in math should consider taking Duke's Math 203, Basic Analysis I. It is also possible to learn the material by working through standard text, doing most of the problems, preferably in collaboration with a couple of other students and with a faculty member to help out now and then. More advanced 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 R (lots of on-line some documentation is available) or Matlab (a primer is available) easier to use than compiled languages like FORTRAN or C. Homework problems are of the form chapter/problem from the text. Not all of them will be graded, but they should be turned in for comment; Tuesday classes will begin with a class solution of one or 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, last revised , and will almost surely be superceded- RELOAD your browser for the current version.
Course grade is based on homework (20%), in-class midterm exam(30%), and take-home final exam (50%).
My rules about auditors are that a student can sit in on or (preferably) audit a course if: