**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.

- 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.

- 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.