| Prof: | Robert L. Wolpert | wolpert@stat.duke.edu | OH: Mon 3:00-4:00pm, 211c Old Chem | ||
| TA: | Mary Beth Broadbent | meb67@stat.duke.edu | OH: Wed 6:00-7:30pm, 211a Old Chem | ||
| Class: | Tue/Thu 11:40-12:55 | & Fri 2:30-3:30pm (Real Analysis) | |||
| Text: | Sidney Resnick, | A Probability Path | Additional references | ||
| Opt'l: | Patrick Billingsley, | Probability and Measure (3/e) | (a classic) | ||
| Jacod & Protter, | Probability Essentials | (easier than Resnick, $36) | |||
| Rick Durrett, | Probability Theory & Examples (4/e) | (more complete) | |||
| Week | Topic | Homework | |
|---|---|---|---|
| I. Foundations of Probability | Problems | Due | |
| Aug 30-01 | Probability spaces: Sets, Events, and σ-Fields | hw1 | Sep 08 |
| Sep 06-08 | Construction & extension of Measures | hw2 | Sep 15 |
| Sep 13-15 | Random variables and their Distributions | hw3 | Sep 22 |
| Sep 20-22 | Expectation & the Lebesgue Theorems | hw4 | Sep 29 |
| Sep 27-29 | Inequalities, Independence, & Zero-one Laws | hw5 | Oct 07 |
| Oct 04-06 | Convergence concepts: a.s., i.p., Lp, Loo | hw6 | Oct 18 |
| --- Fall Break (Oct 08-11) --- | |||
| Oct 13 | Uniform Integrability | hw7 | Oct 27 |
| Oct 18-20 | Review & in-class Midterm Exam (Thu Oct 20) | '07, '08, '10 | Results |
| Oct 25-27 | Strong & Weak Laws of Large Numbers | hw8 | Nov 03 |
| II. Convergence of Distributions | |||
| Nov 01-03 | Convergence in Dist'n, CLT, & Stable Limits | hw9 | Nov 10 |
| Nov 08-10 | Extremes (notes) | hw10 | Nov 17 |
| III. Conditional Probability & Expectation | |||
| Nov 15-17 | Radon-Nikodym thm and conditional probability | hw11 | Dec 02 |
| Nov 22 | Stein's Method (time permitting) | ||
| --- Thanksgiving Break (Nov 23-27) --- | |||
| Nov 29-01 | Martingales and Markov Chains | ||
| Dec 13 | Take-home Final Exam due 9am ('06, '07, '10) | Hists: exam, course | |
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. Try to answer the questions on this diagnostic analysis quiz to see if you're prepared. Most students who majored in mathematics will be familiar with this material; but students with less background in math should consider taking Duke's Math 531 (203), Basic Analysis I: F09 vsn before taking this course. It is also possible to learn the material by working through one of the standard texts and 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 may be omitted.
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 superseded— 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%).
Unregistered students are welcome to sit in on or (preferably) audit a course if: