Course: MATH 170B, Probability Theory II, Winter 2017
Prerequisite: Math 170A.
Course Content: Convergence of random variables, laws of large numbers, central limit theorem, Bernoulli process, Poisson process.
Last update: 21 March 2017

Instructor: Steven Heilman, heilman(@-symbol)
Office Hours: Fridays 830AM-930AM, Mondays 10AM-11AM, MS 5634
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 1PM-150PM, Geology 6704
TA: Yunfeng Zhang, zyf(@-symbol)
TA Office Hours: Mondays 3PM-4PM, Wednesdays 4PM-5PM, MS 3955
Discussion Session Meeting Time/Location: Thursdays, 1PM-150PM, MS 5118
Required Textbook: D. P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2nd edition. (The 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, January 30, 1PM-150PM, Public Affairs 1246
Second Midterm: Friday, February 24, 1PM-150PM, Boelter 2444
Final Exam: Tuesday, March 21, 3PM-6PM, Geology 3656
Other Resources: 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, here and here are sites with practice exams from other 170B classes. Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order.

Homework Policy: Grading Policy:

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

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

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Homework Exam Solutions Supplementary Notes