Rob Thompson Courant Institute NYU

Tuesday/Thursday 6:00-8:20 Room: Online

May 26-July 2, 2019

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

**Office:** http://zoom.us/my/profthompson **Hours:** TTh 5:00-6:00pm

- You won't be expected to solve a linear difference equation
- There won't be anything on Markvov chains on the final.

- practice problems
- Solutions to the practice problems
- Practice problems for the final exam
- Solutions to the practice problems for the final exam

- Lecture May 28, part I
- Lecture May 28, part II
- Lecture June 2
- Lecture June 4
- Lecture June 9
- Lecture June 11
- Lecture June 16
- Lecture June 18
- Lecture June 23
- Lecture June 25
- Lecture June 30

- Assignment One, due Tuesday, June 2:

1.3/1,2

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 Friday, 6/12:

3.3/1,5

3.5/3

3.11/3,6,8,10 - Assignment Two Addendum, due Tuesday, 6/16.
- Assignment Three, due Thursday, 6/18:

4.1/1,2

4.3/1,5

4.4/1,3,5

4.8/3,5a - Assignment Four

4.7/8,10 and Assignment Four Addendum, due Sunday June 28. - Assignment Five

6.1/2

6.2/2,3

6.3/2

and Assignment Five Addendum, due Thursday, 7/2, except that problems 2 and 3 of the addendum are not required to be handed. You may hand them in for extra credit.

- Assignment One Solutions.
- Assignment Two Selected Solutions.
- Assignment Three, selected solutions.
- Assignment Four Addendum, solutions.

**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 a lot of the material from 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. The first assignment is due on June 2.**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 %.

- Probability spaces, events, probability: 1.1-1.4
- Independence, random variables, discrete random variables: 1.5,2.1-2.5,3.1,3.2
- Expectation, Gambler's Ruin: 3.3,3.5,3.6,3.8,3.9
- Conditional distributions and conditional expectation, 3.7
- Continuous random variables, 4.1-4.4
- More on continuous random variables, 4.4,4.5,4.8
- Conditional distributions, functions of random variables, 4.6, 4.7
- More on functions of random variables, 4.7,moment generating functions (see 5.7)
- Central Limit Theorem (see 5.10)
- Markov chains, Chapter 6
- More on Markov chains, Chapter 6

The following are sections from the book that we are

- 1.6,2.6,3.4,3.10,4.9-4.13,Much of Chapter Five, Most of Chapter 6.

- Assignment One, due Tuesday, June 2:

1.3/1,2

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

- 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