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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.