Math 492 - Probability II
Spring 2010

Instructor: Elizabeth Meckes

Office: Yost 208

Phone: 368-5015

Email: ese3 [at] cwru.edu

Office Hours: MTF 11:00 - 12:00, or by appointment

Textbook: Probability and Measure, 3e by Patrick Billingsley

Topics: We will start with chapter 6 (the Radon-Nikodym derivative and conditional probability). We'll then do a unit on Stein's method for distributional approximation, focusing on Poisson approximation and normal approximation. Then we'll do section 8 of the text book, which is basic Markov chain theory. Then we'll do chapter 7 (stochastic processes), and finally finish out the term with more advanced topics on Markov chain theory.

Grading: I expect you to attend the lectures, take notes (much of the material is not in the text), and read the text book on the topics we cover from it. This book is very thorough and well-written, and will be a valuable resource for the course. There will be student presentations (worth 30% of the course grade) and weekly homework assignments (worth 70%). Selected homework problems will be graded.

Homework Problems: Doing the homework problems is probably the single biggest factor in determining how much you get out of the course. If you are having trouble with the problems, please come ask for help; you will learn much more (and probably get a rather better grade) if you figure out all of the homework problems, possibly with help in office hours, than if you do them alone when you can and skip the ones you can't. Homework is weekly, due at the beginning of class on Wednesdays. I strongly suggest starting early so that there is time to ask for help if you need it. In particular, office hours are MTF so that you can get started in time to ask initial questions on Friday, work hard over the weekend, and then have the opportunity to ask more questions Monday and Tuesday before turning in the assignment on Wednesday. Problems will be posted below; selected problems will be graded. You may discuss the homework with other students, however, you must write up solutions on your own.

Assignments: Problems are numbered as n.m, with n being the section number and m the problem number. When a problem has an up arrow indicating that previous results are needed, you may use them without proof.
For January 20:
32.3, 32.5, 32.6, class problem.
For January 29 (please email me your solutions):
33.2, 33.3., 33.4, 33.7.
For February 10:
33.13, 34.2 34.3, 34.10.
For February 17:
34.16, 34.17, 35.4, 35.6.
For February 24:
35.9, 35.14, Additional Problems
For March 3:
Problems
For March 31:
36.1, 36.2, 36.4, 37.1.
For April 7:
Class problem, 37.5, 37.6, 37.7.
For April 14:
37.9, 37.10, 37.11, 37.12(a).
For April 28:
Problems