Download Syllabus - UMass Math

STATISTICS 605
Instructor:
Office, Phone, Email:
Professor Hongkun Zhang
Room 1340 LGRT — telephone: 545-2871
[email protected]
Web Page:
http://www.math.umass.edu/~hongkun
Dept. Phone:
545-2762 or 545-0510
Mailbox:
16th floor, opposite Room 1623E
Office Hours:
Monday: 3:00pm – 4:00 p.m, Thursday 11:00-12:00
Text:
Probability: Theory and Examples by Rick Durrett, 2010
http://www.math.duke.edu/~rtd/PTE/pte.html
Grading:
Your grade will be based on your performance on the
assignments and on your classroom participation.
Other References:
CallNumber
QA273 .B864
QA273 .C577 2001
Author
Breiman, Leo
Chung, Kai Lai
QA273 .F3712 1968 v.1 c.3
Feller, William
QA273 .F3712 1957 v.2
Feller, William
Jeffrey Rosenthal
Title
Probability
A Course in Probability Theory
An Introduction to Probability Theory
and Its Applications, volume 1
An Introduction to Probability Theory
and Its Applications, volume 2
A first look at rigorous probability Th.
Description: The subject matter of probability theory is the mathematical analysis of
random events, which are empirical phenomena having some statistical regularity but not
deterministic regularity. The theory combines aesthetic beauty, deep results, and the ability
to model and to predict the behavior of a wide range of physical systems as well as systems
arising in technological applications. In order to properly handle applications involving
continuous state spaces, a measure-theoretic treatment of probability is required. The
purpose of this course is to present such a treatment, which is based on Kolmogorov’s
axiomatic approach. Topics to be covered include the following:
• Random variables, expectation, independence, laws of large numbers, weak
convergence, central limit theorems, and large deviations.
• The concepts of conditional probability and conditional expectation.
• Basic properties of certain classes of random processes such as martingales and
random walks.