Course: MATH 170B, Probability Theory 2, Lecture 2, Fall 2017
Prerequisite: Math 170A.
Course Content: Convergence of random variables, laws of large numbers, central limit theorem, Bernoulli process, Poisson process.
Last update:10 October 2017

Instructor: Steven Heilman, heilman(@-symbol)ucla.edu
Office Hours: Mondays, 10AM-12PM, MS 5346
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 9AM-950AM, MS 5137
TA: Tyler Arant, tylerarant(@-symbol)math.ucla.edu
TA Office Hours: Tuesdays 930AM-11AM, MS 2361
Discussion Session Meeting Time/Location: Thursday, 9AM-950AM, MS 5137
Recommended Textbook: D. P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2nd edition. (This book is freely available online, though some sections are ordered differently than the textbook.)
Other Textbooks (not required): Elementary Probability for Applications, Durrett, (or a more advanced text for someone who has at least taken 115a and 131a:) Probability: Theory and Examples, Durrett.

First Midterm: Monday, October 23, 9AM-950AM, Haines A2
Second Midterm: Friday, November 17, 9AM-950AM, Haines A2
Final Exam: Monday, December 11, 1130AM-230PM, Location TBD
Other Resources: Supplemental Problems from the textbook. An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Email Policy:

Exam Procedures: Students must bring their UCLA ID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the UCLA Student Guide to Academic Integrity. If you are an OSD student, I would encourage you to discuss with me ways that I can improve your learning experience; I would also encourage you to contact the OSD office to confirm your exam arrangements at the beginning of the quarter.
Exam Resources: Here are my exams from the winter quarter of 2017: Exam 1 Exam 1 Solution Exam 2 Exam 2 Solution Final Final Solution. Here and here are pages containing practice exams for other 170b classes. Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order, but generally, the concepts should be close.

Homework Policy: Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
0 Sep 29: Introduction
1 Oct 2: Review of Probability Oct 4: 4.1, Derived Distributions Oct 5: Homework 0 (ungraded) Oct 6: 4.2, Covariance
2 Oct 9: 4.3, Conditional Expectations Oct 11: 4.3, Conditional Variance Oct 12: Homework 1 due Oct 13: 4.4, Moment Generating Function
3 Oct 16: 4.4, Fourier Transform Oct 18: 4.2 Convolution Oct 19: Homework 2 due Oct 20: 4.4, Random Sums of Random Variables
4 Oct 23: Midterm #1 Oct 25: 7.1, Markov and Chebyshev Inequalities Oct 26: Homework 3 due Oct 27: 7.2, Weak Law of Large Numbers
5 Oct 30: 7.3, Convergence in Probability Nov 1: 7.4, Central Limit Theorem Nov 2: Homework 4 due Nov 3: 7.4, Central Limit Theorem
6 Nov 6: 7.5, Strong Law of Large Numbers Nov 8: 7.5, Strong Law of Large Numbers Nov 9: Homework 5 due Nov 10: No class
7 Nov 13: 7.5, Strong Law of Large Numbers Nov 15: 5.1, Bernoulli Process Nov 16: Homework 6 due Nov 17: Midterm #2
8 Nov 20: 5.1, Bernoulli Process Nov 22: 5.2, Poisson Process No class Nov 24: No class
9 Nov 27: 5.2, Poisson Process Nov 29: 5.2, Poisson Process Nov 30: Homework 7 due Dec 1: Random Walks
10 Dec 4: Optional Stopping Theorem Dec 6: Leeway Dec 7: Homework 8 due Dec 8: Review of Course

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Homework Supplementary Notes