Statistics 330/600 (Spring 2006)

Advanced Probability

Instructor: David Pollard (
When: Tuesday, Thursday 2:30 - 3:45
Where: 113 WLH
Office hours: Wednesday 1:00 - 2:20 (more if needed)
TA:Cong Huang (
Problem session:tba

Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis is assumed.

Intended audience

The course is aimed at students (both graduate and undergraduate) who are either comfortable with real analysis or who are prepared to invest some extra effort to learn more real analysis during the course. Prior exposure to an introductory probability course (such as Stat 241/541) would be an advantage, but is not essential.

Knowledge of measure theory is not assumed. The first two weeks of the course will introduce key measure theoretic ideas, with other ideas explained as needed.


Pollard, User's Guide to Measure Theoretic Probability
Cambridge University Press 2001. [Table of contents].
Labyrinth Bookstore should also have some copies.

If you prefer a more standard text, one of the books on the list of references might be to your taste.


Coverage similar to the description at the end of the Preface.


The final grade will be based entirely on the weekly homework.

Students who wish to work in teams (no more than 3 to a team) should submit a single a solution set. All members of a team will be expected to understand the team's solutions sufficiently well to explain the reasoning at the blackboard. Occasional meetings with DP will be arranged.

Homework due each Thursday

Handouts, including some extracts from UGMTP and rewrites of UGMTP.

Class materials for an introductory probability course (Stat 241/541, Fall 2000), containing more extensive elementary discussion of probabilistic ideas. See, in particular, the Chapters 2 and 4, on conditional expectations and on symmetry.

DBP 24 Jan 2006