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
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).
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.
