Statistics 205B: Probability Theory (Spring 2008)
Instructor: Elchanan Mossel (mossel@stat)
Class Time: 9:30am11:00am on TuTh at 330 Evans.
Instructor Office hours: Wednesday 9:00am11:00am, 423 Evans.
GSI: Partha S. Dey (partha@stat)
GSI Office hours: Tuesday 1:00pm3:00pm, 387 Evans.
Textbook: Probability: Theory and Examples (3rd Edition) by Richard Durrett.
Reference: Foundations of Modern Probability (2nd Edition) by Olav Kallenberg.
Announcements
 X_{1}, X_{2}, X_{3}, ... are i.i.d. in problem 4, HW13.
 In HW11, for problem 3 and 4 you can assume that : Given two probability measures μ,ν on a finite space Ω, there exists a coupling such that Ed(X,Y)=d_{K}(μ,ν). One can prove this easily using continuous function and compactness argument.
 In HW11, for problem 4, you can use the result that
d_{K}(αμ_{1} +(1α)μ_{2},αν_{1} +(1α)ν_{2}) ≤ αd_{K}(μ_{1},ν_{1}) +(1α)d_{K}(μ_{2},ν_{2}).
The proof uses appropriate coupling.  hw10.pdf has been updated. There are some more hints and clarifications.
 Additional condition in HW 8: In problem #5 assume that E[X_{i}(1)] = E[X_{i}(2)] = 0.
 Clarifications and corrections in HW 7: In problem #1 you have to provide an instance where each of the theorems have been used. In problem #3 show that γ ≤ e. In problem #4 the edges connect (m,n) to (m1,n1) and (m+1,n1) and the water starts flowing from (0,0).
Homework
Here is the Homework Policy

