| Prof: | Robert L. Wolpert | wolpert@stat.duke.edu | OH: Mon 4:15-5pm, 211c Old Chem (684-3275) | ||
| TA: | Danilo Lopes | dll11@stat.duke.edu | OH: tba | ||
| 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 07 | Introduction: Probability spaces, outcomes, events | ||
| Jan 12,14 | Probability spaces: fields and sigma-fields | hw1 | Jan 21 |
| Jan 21 | Probability spaces: Constructing & extending measures | hw2 | Jan 28 |
| Jan 26-28 | Random variables and their distributions | hw3 | Feb 11 |
| Feb 02-04 | No class (NSF Panel) | ||
| Feb 09-11 | Integration & expectation: Lebesgue's MCT & DCT | hw4 | Feb 18 |
| Feb 16-18 | Independence & zero-one Laws: Fubini's Thm | hw5 | Feb 25 |
| II. Convergence of Random Variables & Distributions | |||
| Feb 23-25 | Convergence concepts: a.s., i.p., Lp, Loo | hw6 | Mar 04 |
| Mar 02-04 | Markov, Chebychev, Hoeffding, and UI | hw7 | Mar 16 |
| --- Spring Break (Mar 07-15) --- | |||
| Mar 16-18 | Review and in-class Midterm (Wed Mar 18) '05, '06, '07, '08 | Results | |
| Mar 23-25 | Strong & weak laws of large numbers | hw9 | Apr 01 |
| Mar 30-01 | Convergence in distribution & C.L.T. | hw10 | Apr 08 |
| Apr 06-08 | Stable limit theorem & ID limits (notes) 101 Old Chem | hw11 | Apr 15 |
| III. Conditional Prob & Expectation | |||
| Apr 13-15 | Radon-Nikodym thm and conditional probability | MGs | |
| Apr 29 | Take-home Final Exam (due 2pm) '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: