| Prof: | Robert L. Wolpert | 211c Old Chem (684-3275) wolpert@stat.duke.edu | ||
| Class: | Tue & Thu 12:40-1:55pm | 025 Old Chem | ||
| OH: | Wed 2:00-4:00pm | |||
| Text: | Sidney Resnick, | A Probability Path | ||
| Opt'l: | Patrick Billingsley, | Probability and Measure (3rd edn) | ||
| Additional references |
| Week | Topic | Homework Problems | |
|---|---|---|---|
| I. Foundations of Probability | |||
| Jan 9 | Probability spaces: sets, events, and sigma-fields | 1/1,3,4,12,24,39 | |
| Jan 14-16 | Probability spaces: Constructing & extending measures | 2/8,11,14,19 | |
| Jan 21-23 | Random variables and their distributions (notes) | 3/2,3,6,15 | |
| Jan 28-30 | Independence, product spaces, & Fubini's theorem I | 4/1,2,4,7,8,9,10,11 | |
| Feb 4-6 | Independence, product spaces, & Fubini's theorem II | 4/13,16,18,19,21,24,28 | |
| Feb 11-13 | Integration & expectation I | 5/1,4,7, 16, 17 | |
| Feb 18-20 | Integration & expectation II | 5/19,21,24,29,32 | |
| Feb 25-27 | Review and in-class Midterm Exam (Thu Feb 27) | ||
| II. Convergence of Random Variables & Distributions | |||
| Mar 4-6 | Convergence concepts: a.s., i.p., Lp, Loo | 6/5,7,8,10,13,14,17,30 | |
| --- Spring Break (Mar 8-16) --- | |||
| Mar 18-20 | Strong & weak laws of large numbers | 7/1,4,8,43,44,46 | |
| Mar 25-27 | Convergence in distribution & C.L.T. | 8/2,3,12; 9/5,6,9,10 | |
| Apr 1-3 | Stable limit theorem & ID limits (notes: ps, pdf) | ||
| III. Conditional Prob & Expectation | |||
| Apr 8-10 | Radon-Nikodym thm and conditional probability | 10/6,7,8,10,13 | |
| Apr 15-17 | Foundations of Bayesian statistics | ||
| Apr 29 | Take-home Final Examination (due 7pm). | ||
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 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.