| Profs: | Robert L. Wolpert | 211c Old Chem (684-3275) wolpert@stat.duke.edu | ||
| Athanasios Kottas | 221 Old Chem (684-8025) thanos@stat.duke.edu | |||
| Class: | Mon & Wed 2:20-3:35pm | 128 Soc/Psych | ||
| OH: | Tue 3:00-4:00pm | |||
| Texts: | Patrick Billingsley, | Probability and Measure (3rd edn) | ||
| Additional references |
| Week | Topic | Homework Problems |
|---|---|---|
| I. Foundations of Probability | ||
| Jan 9 | Probability spaces: sigma-fields and probability measures | |
| Jan 21 | The Borel-Cantelli lemmas | |
| Jan 28 | Random Variables and distribution functions | |
| Feb 4 | Expectation and inequalities | |
| Feb 11 | Extension of measures | |
| Feb 18 | Lebesgue integration, Fatou's lemma | |
| II. Convergence of Random Variables & Distributions | ||
| Feb 25 | Independence, Product Spaces, & Fubini's Theorem | |
| Mar 4 | Convergence of sequences of Random Variables | |
| --- Spring Break (Mar 9-17) --- | ||
| Mar 18 | - Class postponed due to ENAR - | |
| Mar 25 | Strong Law of Large Numbers, Weak Convergence | HW1 Due Apr 3 (ps, pdf) |
| Apr 1 | Central Limit Theorem | |
| Apr 8 | Stable Limit Theorem & ID Limits (notes: ps, pdf) | |
| III. Conditional Prob & Expectation | ||
| Apr 15 | Radon-Nikodym and Conditional Probability | HW Due Apr 24 |
| Apr 22 | Markov Procs, Martingales, and Brownian Motion | |
| Apr 29 | Final Examination (due 5pm). | |
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 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; Monday 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.