## MATH-GA 2901 Basic Probability Summer 2017

Rob Thompson Courant Institute NYU

Tuesday/Thursday 6:00-8:20 Room: CIWW 512

May 23-June 29, 2017

**e-mail:**
robert.thompson@hunter.cuny.edu

**Office: ** CIWW 508 **Hours:** TTh 5:00-6:00

### Basic Information About the Course:

**Text:** The text for this course is *Probability and Random Processes*, 3rd edition, by
Geoffrey Grimmett and David Stirzaker, Oxford University Press. We
will cover the first five chapters and portions of the sixth and
thirteenth chapter of the text. Topics will include probability
spaces, random variables, probability distributions, generating
functions, law of large numbers and the central limit theorem, random
walks, discrete and continous Markov processes.

**Prerequisites:** The prerequisites for this course are
single variable and multivariable calculus, including sequences and
series, partial derivatives and multiple integrals.

**Exams:** We will have a small quiz, a one hour midterm
exam, and a two hour final exam. There will be NO MAKEUPS. The final
exam will be on the last day of class. The final exam will
be cumulative, but skewed toward the last half of the term.

**Homework:** The homework
will be due once a week. I will post the homework assignments on the
course webpage

**Grading:** The quiz will be worth 10 % of your grade,
the midterm exam is worth 30 %, the final exam is worth 45 %, and
the homework is worth 15 %.

###
Quiz

The quiz will be this Thursday, June 1.
The quiz will be 30 minutes long and will be on the material represented on the first homework assignment.
###
Midterm Exam

The midterm will be on Tuesday, June 20.
The topics covered on the midterm are:
- 1.1-1.5
- 2.1,2.3
- Gambler's Ruin, 3.1,3.2,3.3,3.5
- 4.1-4.4
- 4.7,4.8

Here are the solutions to the midterm exam.
###
The Homework Assignments

- Assignment One, due Tuesday, May 30:

1.3/1

1.4/3

1.5/1,2,9

1.8/1,4,15,22,30,33

2.1/2

2.7/7,8

3.1/3
- Assignment Two, due Tuesday, 6/6:

3.3/1,5

3.5/3

3.11/3,6,8,10
- Assignment Two Addendum,
due Thursday, 6/8
- Assignment Three, due Thursday, 6/15:

4.1/1,2

4.3/1,5

4.4/1,3,5

4.8/3,5a
- Assignment Four, due Thursday, 6/22:

4.7/8,10 and

Assignment
Four Addendum, due Tuesday 6/27.
- Assignment Five, due Friday, 6/30:

6.1/2

6.2/2,3

6.3/2

and
Assignment
Five Addendum, due Friday, 6/30.

###
Homework Solutions

###
Practice Problems and Solutions

###
Other Solutions

###
Some Other References

- Here is a link to a tutorial on solving second order linear
difference equations. This is relevant to the Gambler's Ruin
Problem on Assignment Two.
- A First Course in Probability, Sheldon M. Ross
- Introduction to Probability Models, Sheldon M. Ross