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.
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:
- 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.
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 |
| 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.
Homework
Exam Solutions
Supplementary Notes