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.
- 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) ≤ αdK(μ1,ν1) +(1-α)dK(μ2,ν2).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).
Here is the Homework Policy
There are weekly homework assignments. Homework problems are mostly drawn from the text [Du] Probability: Theory and Examples (3rd ed) by Rick Durrett. Here are the ground rules.
- Due date: Homework from Week n is due Thursday of Week n+1 in class.
- Scoring: Each homework consists of about 5 exercises though the exact number may vary. Each week, depending on class size, I will sample arbitrarily between 2 and 5 of them and I will grade only those problems (same problems for everyone). Also the problems marked with * will be always graded. Each homework will be graded on 20 points.
- Three-strike policy: There will be roughly 12 homeworks. At the end of the semester, two of them will be dropped from your final grade (typically the lowest two grades). If on a particular week, you are unable to produce a homework assignment for any reason, that homework will count as one of the two dropped assignments.
A few more remarks about homeworks.
- No late homework: Homeworks are due at the beginning of class every Thursday. Late homeworks will not be accepted. (But see the Three-Strike Policy.)
- Group work: You are welcome to work on the problems in groups. But each student must submit their own solutions.
- Hints: No hints will be given at office hours.