Lecture 3: Independence and Borel-Cantelli lemmas

Reading: Resnick - Chapter 4; Koski - Section 1.6 and 1.7

Lecture notes: Lecture 3.pdf

Suggested problems:
E-level: Resnick 4.6:1, 4.6:3, 4.6:7, 4.6:14*, 4.6:20, 4.6:29
C-level: Resnick , 4.6:2, 4.6:6*, 4.6:12, 4.6:13, 4.6:17, 4.6:28
A-level: Resnick, 4.6:5, 4.6:15, 4.6:30, 4.6:32,

Lecture 4: Integration, expected value, dominated convergence, monotone convergence
Lecture 5: Product measure, Fubini's theorem, Examples

Reading: Resnick - Chapter 5; Koski - Section 1.8
Lecture notes: Lecture 4.pdf Lecture 5.pdf

Suggested problems:
E-level: Resnick 5.10:1, 5.10:2, 5.10:11*, 5.10:26, 5.10:32
C-level: Resnick , 5.10:4, 5.10:5, 5.10:10, 5.10:13, 5.10:17*, 5.10:22*, 5.10:24, 5.10:29, 5.10:31, 5.10:33, 5.10:35
A-level: Resnick, 5.10:16, 5.10:23, 5.10:30, 5.10:37

Koski 1.12.3.6 , 1.12.3.10

Exercise 2,3:

Resnick: 4.6:6, 4.6:14, 5.10:11, 5.10:17, 5.10:22

Exercise 2.pdf

Exercise 3.pdf, Measurability Exercise 3.pdf (Proof of measurability of the set {(t,w):X(w)>t} with respect to the product sigma-algebra)