Probability Theory, Lecture 3, Winter 2016

Course: MATH 170A, Probability Theory, Lecture 3, Winter 2016
Prerequisite: Math 32B and Math 33A. Not open to students with credit for Electrical Engineering 131A or Statistics 100A.
Course Content: Probability distributions, random variables and vectors, expectation.
Last update: 15 March 2016

Instructor: Steven Heilman, heilman(@-symbol)ucla.edu
Office Hours: Mondays 10AM-11AM, Fridays, 9AM-10AM, MS 5634
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 1PM-150PM, MS 6229
TA: Adam Haque, adamhaque12(@-symbol)math.ucla.edu
TA Office Hours:Wednesdays 4PM-5PM, Thursdays, 10AM-11AM, 2PM-3PM, MS 3975
Discussion Session Meeting Time/Location: Thursday, 1PM-150PM MS 6229
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: Friday, January 29th, 1PM-150PM, Pub Aff 2214
Second Midterm: Monday, February 22nd, 1PM-150PM, Bunche 1209B
Final Exam: Tuesday, March 15, 8AM-11AM, KNSY PV 1200B
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:

My email address for this course is heilman(@-symbol)ucla.edu
It is your responsibility to make sure you are receiving emails from heilman(@-symbol)ucla.edu , and they are not being sent to your spam folder.
Do NOT email me with questions that can be answered from the syllabus.

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 is a page containing old exams for another 170A class. Here is a 170A practice midterm (with solutions). Here is a 170a practice second midterm. Here is a 170A practice final. 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 if not identical.

Homework Policy:

Late homework is not accepted.
If you still want to turn in late homework, then the number of minutes late, divided by ten, will be deducted from the score. (The time estimate is not guaranteed to be accurate.)
The lowest two homework scores will be dropped. This policy is meant to account for illnesses, emergencies, etc.
Do not submit homework via email.
There will be 8 homework assignments, assigned weekly on Thursday and turned in at the beginning of the discussion section on the following Thursday.
A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
You may use whatever resources you want to do the homework, including computers, textbooks, friends, the TA, etc. However, I would discourage any over-reliance on search technology such as Google, since its overuse could degrade your learning experience. By the end of the quarter, you should be able to do the entire homework on your own, without any external help..
All homework assignments must be written by you, i.e. you cannot copy someone else's solution verbatim.
Homework solutions will be posted on Friday after the homework is turned in.

Grading Policy:

The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%). The grade for the semester will be curved. However, anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
We will use the MyUCLA gradebook.
If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
You must attend the final exam to pass the course.

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

Week	Monday	Tuesday	Wednesday	Thursday	Friday
1	Jan 4: 1.1, Sets		Jan 6: 1.2, Probabilistic Models	Jan 7: Homework 0 (ungraded)	Jan 8: 1.2, Probabilistic Models
2	Jan 11: 1.3, Conditional Probability		Jan 13: 1.3, Conditional Probability	Jan 14: Homework 1 due	Jan 15: 1.4, Total Probability Theorem and Bayes' Rule
3	Jan 18: No class		Jan 20: 1.5, Independence	Jan 21: Homework 2 due	Jan 22: 1.5, Independence
4	Jan 25: 1.6, Counting		Jan 27: 2.1, Discrete Random Variables	Jan 28: Homework 3 due	Jan 29: Midterm #1
5	Feb 1: 2.2, Probability Mass Function		Feb 3: 2.3, Functions of Random Variables	Feb 4: Homework 4 due	Feb 5: 2.4, Expectation and Variance
6	Feb 8: 2.5, Joint PMFs, Covariance and Variance		Feb 10: 2.6, Conditioning	Feb 11: Homework 5 due	Feb 12: 2.6, Conditioning
7	Feb 15: No class		Feb 17: 2.7, Independence	Feb 18: Homework 6 due	Feb 19: 2.7, Independence
8	Feb 22: Midterm #2		Feb 24: 3.1, Continuous random variables and PDFs	Feb 25: No homework due	Feb 26: 3.1, Continuous random variables and PDFs
9	Feb 29: 3.2, Cumulative Distribution Functions		Mar 2: 3.3, Normal Random Variables	Mar 3: Homework 7 due	Mar 4: 3.4, Joint PDFs of Multiple Random Variables
10	Mar 7: 3.5, Conditioning		Mar 9:3.5, Conditioning	Mar 10: Homework 8 due	Mar 11: 3.6, The Continuous Bayes Rule

Advice on succeeding in a math class:

Review the relevant course material before you come to lecture. Consider reviewing course material a week or two before the semester starts.
When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
Come to class with questions, so you can get more out of the lecture. Also, finish your homework at least two days before it is due, to alleviate deadline stress.
Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes. Also, consider typesetting your homework. Here is a template .tex file if you want to get started typesetting.
If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

Homework

HW0 HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 (Solutions posted on CCLE)

Exam Solutions

Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions Final Final Solutions

Supplementary Notes

Math 170A Lecture Notes