| Class: | Mon & Wed 2:20-3:35pm | 025 Old Chem | ||||
| Prof: | Robert L. Wolpert | rlw@stat.duke.edu | 211c Old Chem (684-3275) | Thu 3:00-4:00pm | ||
| TAs: | Jason Duan | jason@stat.duke.edu | 214d Old Chem (681-9390) | Tue 4:00-5:00pm | ||
| Zhenglei Gao | zhenglei@stat.duke.edu | 112 Old Chem (684-4365) | Tue 6:00-7:00pm | |||
| Text: | Kai Lai Chung, | A First Course in Probability Theory (3rd edn) | ||||
| Opt'l: | Patrick Billingsley, | Probability and Measure (3rd edn) | ||||
| Additional references | ||||||
| Week | Topic | Homework Problems | Due | |
|---|---|---|---|---|
| I. Foundations of Probability | ||||
| Jan 7 | Probability spaces: sets, events, and sigma-fields | 2.1/5,8 Pi-Lam Notes | Jan 14 | |
| Jan 12-14 | Constructing & extending probabilities (notes) | 2.2/1,2,4, 11,16,20,25 | Jan 21 | |
| Jan 21 | Random variables and their distributions | 3.1/3,4,5,10,11 | Jan 28 | |
| Jan 26-28 | Integration & expectation I (UI notes) | 3.2/2,7,17,19 | Feb 6 | |
| Feb 2-4 | Integration & expectation II | |||
| Feb 9-11 | Independence, product spaces, & Fubini's thm | 3.3/2,4,6 | Feb 18 | |
| Feb 16 | In-class Midterm Exam I (Mon Feb 16) | (2003, 2004 vsns)|||
| II. Convergence of Random Variables & Distributions | ||||
| Feb 18 | Converge concepts: a.s., i.p. | 4.1/5,7,8,10 | Feb 25 | |
| Feb 23-25 | Converge concepts: Lp, Loo | 4.2/4,7,12; 4.3/3 | Mar 3 | |
| Mar 1-3 | Convergence concepts: vg. | 4.4/1,4,6; 4.5/1,3,6,7,8 | Mar 17 | |
| --- Spring Break (Mar 6-14) --- | ||||
| Mar 15-17 | Strong & weak laws of large numbers | 5.4/8 Cancelled | ||
| Mar 22-24 | In-class Midterm Exam II (Wed Mar 24) | (2003 vsn)|||
| Mar 29-31 | The Central Limit Theorem | 5.4/8, 6.4/24, 7.4/1-3 | Apr 9 | |
| III. Conditional Probability & Expectation | ||||
| Apr 5-7 | Radon-Nikodym thm and conditional probability | 9.1/2,3,5,10,13 | Apr 16 | |
| Apr 12-14 | Foundations of Bayesian stats? Markov chains? | |||
| May 1 | Take-home Final Examination (due 2pm). | (2003 vsn) | ||
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 the R or S-Plus dialects of S (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; 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.