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Bonus problems are posted on Blackboard. You are also invited to present your solutions in class on Apr 24, 26, 29, or May 1.

This is the web page of 36-752 in Spring 2013. It is being updated constantly. Please check frequently for updates.

Course title: Advanced Probability Overview

Instructor: Jing Lei. Office: 132C BH. Email: jinglei [at] andrew [dot] cmu [dot] edu. Office Hours: Monday 11-12 or by appointment

TA: Lingxue Zhang. Office: GHC 7411. Email: lingxuez [at] andrew [dot] cmu [dot] edu, Office hours: Tuesday 3:30-4:30 in the common area next to GHC 7401

Lecture time and location: WMF 9:30-10:20, PH A22.

Course description:

This is a one-semester course designed to cover two semesters of probability and measure theory. Something will have to give way. Mostly, the proofs will give way. But we will try to prove some of the most important theorems when those proofs illustrate important techniques and concepts. All of the challenging new material in this course will involve limiting operations. If you are uncomfortable with limits or lack intuition about them, this course will be very unpleasant.

Prerequisites Calculus; Real analysis; Undergraduate Probability Theory.

Texts

  1. Probability Theory & Measure Theory, 2nd Ed., by R. Ash and C. Dolèans-Dale
  2. Probability, Theory and Examples, 4th Ed., by R. Durrett.

Syllabus: A pdf file of the syllabus.

Outline

  1. σ-fields, measures, probabilities, extension and uniqueness of probabilities. Lecture Notes Set #1 (updated at 2013-01-13 7:30 pm)
  2. Measurable functions, random variables, distributions, and integration. Lecture Notes Set #2 (updated at 2013-01-22 10:51 pm)
  3. Integration and limits, convergence theorems. Lecture Notes Set #3 (updated at 2013-01-29 10:26 pm)
  4. Radon-Nikodym derivatives; Product spaces and product measures Lecture Notes Set #4 (updated at 2013-02-10 5:30 pm)
  5. Lp space, Weak Law of Large Numbers. Convergence of random variables. Lecture Notes Set #5 (updated at 2013-02-17 11:35 pm)
  6. Almost sure convergence, Strong Law of Large Numbers. Lecture Notes Set #6 (updated at 2013-02-25 8:56 am)
  7. Convergence in distribution. Lecture Notes Set #7 (updated at 2013-03-01 9:10 am)
  8. Characteristic functions and the Central Limit Theorem. Lecture Notes Set #8 (updated at 2013-03-19 11:20 pm)
  9. Conditional probability and expectation. Lecture Notes Set #9 (updated at 2013-03-26 11:00 pm)
  10. Martingales. Lecture Notes Set #10 (updated at 2013-04-12 3:30 pm)

Lecture notes

Lecture notes will be posted (approximately) weekly.

Homeworks

Homework assignments are posted each Wednesday and are due on the following Wednesday in class.
Homework #1 last updated: 2013-01-16 9:05 am
Homework #2 last updated: 2013-01-22 11:00 pm
Homework #3 last updated: 2013-01-29 10:30 pm
Homework #4 last updated: 2013-02-05 10:09 pm
Homework #5 last updated: 2013-02-12 10:00 pm
Homework #6 last updated: 2013-02-20 12:06 am
Homework #7 last updated: 2013-02-26 10:35 pm
Homework #8 last updated: 2013-03-19 11:20 pm
Homework #9 last updated: 2013-03-26 11:00 pm
Homework #10 last updated: 2013-04-03 12:25 am
Homework #11 last updated: 2013-04-09 10:45 pm
Homework #12 last updated: 2013-04-16 11:29 pm

Grade

Homework 30%; Midterm 30%; Final Exam 40%.