# 170B. Probability Theory.

Lectures: MWF 11:00-11:50 in Geology 6704 .

Instructor: Rowan Killip, 6935 Math Sciences Building.

Office Hours: Mon 3:00--4:00pm and Wed 9:00--10:00am in 6935 Math Sciences Building.

Enrolment questions, PTE#, &c: See the math student services office in 6356 Math Sciences Building.

TA: Tianqi Wu.

Exams: One in-class midterm: Wednesday, May 8. Three-hour final: Wednesday, June 12, 8:00am-11:00am.
Bring student ID to both the midterm and the final. There will be no make-up exams.
No calculators, notes, or books will be permitted in any exam.

Homework: There will be weekly homework. It is due in class. Further information is given below.

• No late homework will be accepted.
• Write your name and ID number at the top of the first page.
• Homework will be returned in TA section.
• The weakest homework score will be omitted.

Grading: Homework 20%; Midterm 20%, each; Final 60%.

Syllabus: General Course Outline.

Here are the expected topics of lectures; it will be updated as we progress:

Lecture Section Topics
1-3 4.1 Derived Distributions
4-5 4.2 Correlation
6-7 4.3 Conditional Expectation and Variance (problem 28)
8-9 4.4 Transforms (Handwritten notes)
10 4.5 Sum of a Random Number of Independent RVs.
11 5.1 Markov and Chebyshev Inequalities
12-14 5.2-3 Convergence in probability and in Lp. Weak Law of Large Numbers
15-16 5.4 Convergence in distribution. Central Limit Theorem.
Midterm
17-18 5.5 Almost-sure convergence. Strong Law of Large Numbers (Notes 1 and Notes 2)
19-21 6.1 Bernoulli Process
22-25 6.2 Poisson Process
26-28 Random Walks

Old Exams: In the past I have taught this class with two midterms:
Winter 2017: Midterm 1, Midterm 2
Spring 2017: Midterm 1, Midterm 2
Here is one prior final: Final 2015.

Homework Problems:
Homework 1, due Mon, April 8.
Homework 2, due Fri, April 12.
Homework 3, due Fri, April 19.
Homework 4, due Fri, April 26.
Homework 5, due Fri, May 3.
Homework 6, due Fri, May 10.
Homework 7, due Fri, May 17.
Homework 8, due Fri, May 24.
Homework 9, due Fri, June 7.