**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:*12 December 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, Boelter 2444

**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 Tuesday. - 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 |

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 |

**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.