Matthew L. Wright
Assistant Professor, St. Olaf College

# Probability Theory

## Math 262 ⋅ Spring 2018

Prof. Wright's office hours in RMS 405: Mon. 8:00–8:55 & 2:15–3:15, Wed. 2:30–3:30, Thurs 9:30–10:30, Fri. 10:30–11:30, whenever the door is open, or by appointment

Help sessions: Wednesdays 7–8pm in RNS 204

Friday
February 9
Introduction
What is probability?
Do the following before next class:
Monday
February 12
Sample spaces and events
Axioms of probability
Do the following before next class:
• Finish Homework 1 (due Wednesday at 4pm in the homework mailbox).
Wednesday
February 14
Counting methods
Permutations and combinations
Homework 1
due today
Do the following before next class:
• Begin Homework 2 (due 4pm Monday).
Friday
February 16
More counting methods
Do the following before next class:
Monday
February 19
Conditional probability
Bayes' Theorem
Homework 2
due today
Do the following before next class:
• Begin Homework 3 (due 4pm Friday).
Wednesday
February 21
Independence
Do the following before next class:
Friday
February 23
Simulation of random events
Homework 3
due today
Do the following before next class:
• Begin Homework 4 (due 4pm Wednesday).
• There is no reading assignment for Monday, but this would be a good time to review Chapter 1.
Monday
February 26
Counting Extravaganza
Do the following before next class:
Wednesday
February 28
Random variables
Discrete distributions
Homework 4
due today
Do the following before next class:
• Begin Homework 5. (Note that this homework is not due until Wednesday, March 7, but it is a bit longer than usual.)
Friday
March 2
Expected value
Variance and standard deviation
Do the following before next class:
Monday
March 5
Binomial distribution
Do the following before next class:
• Finish Homework 5 (due 4pm Wednesday).
• There is no reading assignment for Wednesday, but this would be an excellent time to review §2.1–2.4.
Wednesday
March 7
Review for exam
Homework 5
due today
Study for Exam 1.
Friday
March 9
Exam 1
• This exam will cover Sections 1.1 through 1.5 and 2.1 through 2.3.
• Calculators will be permitted, but probably not very helpful, and certainly not necessary.
• Books, notes, and internet-capable devices will not be permitted during the exam.
• A review page, with suggested problems, is available here.
Do the following before next class:
Monday
March 12
Poisson distribution
Do the following before next class:
Wednesday
March 14
Hypergeometric distribution
Homework 6
due today
Do the following before next class:
Friday
March 16
Negative binomial distribution
Geometric distribution
Do the following before next class:
Monday
March 19
Moment generating functions
Homework 7
due today
Do the following before next class:
• Re-read §2.7. This section should make more sense now than the first time you read it. There is no reading guide for Wednesday.
• Begin Homework 8.
Wednesday
March 21
Moment generating functions
Do the following before next class:
• Finish Homework 8.
• If possible, bring a computer with R and RStudio to class on Friday.
Friday
March 23
Simulation of discrete random variables
Homework 8
due today
Have a great spring break! No class March 26 – April 2.
Do the following before next class:
Wednesday
April 4
Continuous random variables
Uniform distribution
Do the following before next class:
Friday
April 6
Expected values and moment generating functions of continuous distributions
Homework 9
due today
Do the following before next class:
Monday
April 9
Normal distribution
Do the following before next class:
Wednesday
April 11
Exponential distribution
Homework 10
due today
Do the following before next class:
Friday
April 13
Gamma distribution
Do the following before next class:
Monday
April 16
Transformations of continuous random variables
Do the following before next class:
• Re-read §3.7, focusing on Examples 3.39–3.41.
• Finish Homework 11.
Wednesday
April 18
Transformation of random variables and review problems
Take-home exam problems distributed
Homework 11
due today
Complete the take-home exam problems before next class.
Friday
April 20
Exam 2
Do the following before next class:
Monday
April 23
Joint distributions
Do the following before next class:
Wednesday
April 25
Expected values
Covariance and correlation
Homework 12
due today
Note: No help session on Wednesday evening this week.
Do the following before next class:
• Read from the beginning of §4.3 up to the §4.3.1 heading (pages 264–268 in the Second Edition of the text). Answer the questions on the Reading Guide.
• Begin Homework 13 (due 4pm Monday).
Friday
April 27
Linear combinations of random variables
Do the following before next class:
Monday
April 30
Properties of linear combinations
Homework 13
due today
Do the following before next class:
Wednesday
May 2
Conditional distributions and expectation
Do the following before next class:
Friday
May 4
Limit theorems
Homework 14
due today
Do the following before next class:
Monday
May 7
Limit theorems
Do the following before next class:
Wednesday
May 9
Transformations of random variables
Distribution function method
Homework 15
due today
Do the following before next class:
• Begin Homework 16.
Friday
May 11
Transformations of random variables
Bivariate transformation theorem
Do the following before next class:
Monday
May 14
Order statistics
Do the following before next class:
Wednesday
May 16
Review day
Homework 16
due today
Complete the take-home portion of the final exam.
Saturday
May 19
Final Exam, 9–11am
• This exam will be cumulative, with emphasis on Chapter 4.
• The exam will consist of an in-class portion and a short take-home portion.
• The take-home portion will be distributed on May 16 and due at the final exam time on May 19. For this portion of the exam you may use your textbook, your notes, the course web site, a calculator, R, Mathematica, and Wolfram Alpha, but not other people, web sites, books, etc. Remember the honor code!
• For the in-class portion: books, notes, and internet-capable devices will not be permitted. Calculators will be permitted, but probably not very helpful, and certainly not necessary.