## Statistics 205B: Probability Theory (Spring 2008)

Instructor: Elchanan Mossel (mossel@stat)

Class Time: 9:30am-11:00am on TuTh at 330 Evans.

Instructor Office hours: Wednesday 9:00am-11:00am, 423 Evans.

GSI: Partha S. Dey (partha@stat)

GSI Office hours: Tuesday 1:00pm-3:00pm, 387 Evans.

Textbook: Probability: Theory and Examples (3rd Edition) by Richard Durrett.

Reference: Foundations of Modern Probability (2nd Edition) by Olav Kallenberg.

### Announcements

• X1, X2, X3, ... 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)=dK(μ,ν). One can prove this easily using continuous function and compactness argument.
• In HW11, for problem 4, you can use the result that

dK(αμ1 +(1-α)μ2,αν1 +(1-α)ν2) ≤ αdK11) +(1-α)dK22).

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[Xi(1)] = E[Xi(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 (m-1,n-1) and (m+1,n-1) and the water starts flowing from (0,0).

### Homework

Here is the Homework Policy

 Homework 13 : Due on 1st May (Solution) Homework 12 : Due on 24th April (Solution) Homework 10 : Due on 10th April (Solution) Homework 8 : Due on 20th March (Solution) Homework 6 : Due on 6th March (Solution) Homework 4 : Due on 21st February Homework 2 : Due on 5th February Homework 13 : Due on 1st May (Solution) Homework 11 : Due on 17th April (Solution) Homework 9 : Due on 3rd April (Solution) Homework 7 : Due on 13th March (Solution) Homework 5 : Due on 28th February (Solution) Homework 3 : Due on 14th February Homework 1 : Due on 29th January