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