Nestor Guillen Department of Mathematics University of California at Los Angeles Office: MS 6903 Email: nestor@math.ucla.edu About Research >Teaching 170A   Links Nonlocal Wiki

Math 170b. Winter 2012

Probability Theory

Lectures: MWF 10:00-10:50 am in MS 5127.
Office hours: Monday 3:30-6:30.

Discussion: Thursday 10:00-10:50 am. In MS 5127.
TA: Choongbum Lee. Email: abdesire@ucla.edu.

For additional information, see the first day handout .

A practice exam for the first midterm is now available, as well as its solutions. Here is also the practice for the second midterm.

NOTE: A practice final exam is now available.

Homeworks

Homework for week x is due on the friday of week x (in particular, the first homework is due on January 13th).

Week 1. Solve problems 5, 18 and 19 in Chapter 3 and problems 5, 7 and 14 in Chapter 4.

Week 2. Chapter 4: Problems 7, 10, 11 and 12.

Week 3. Chapter 4: Problems 17, 19, 23, 32, and 34.

             Extra problem #1: Prove that if X is a real random variable, and f is any convex function, then the expectation of f(X) is no smaller than f evaluated at the expectation of X. Hint: Prove it first for X a discrete variable taking only 2 values, then for a variable taking a finite number of values, how to go from there to the continuum case?

             Study the detailed answers to problems 20,21 and 27.

Week 4. Chapter 4: Problems 36, 37, 41, 42 and 43.

Week 5. Fifth homework .

Week 6. Sixth homework .

Week 7. Seventh homework .

Week 8. Eight homework (also practice midterm) .

Week 9. Chapter 6: Problems 9, 10, 13 and 16. Study the detailed answers to problems 18 and 24.

Week 10. Tenth homework.