Matthew L. Wright
Assistant Professor, St. Olaf College

# Probability Theory

## Math 262 ⋅ Fall 2019

Prof. Wright's office hours in RMS 405: Mon. 9:00–10:00, Tues. 9:30–10:30, Wed. 2:00–3:00, Thurs 1:00–2:00, Fri. 9:00–10:00, whenever the door is open, or by appointment

Friday
September 6
Introduction
What is probability?
Do the following before next class:
• Complete the Syllabus Quiz.
• Read §1.1 and §1.2 (at least through page 10) and answer the questions on the Reading Guide (also on the back of your worksheet from class). Bring your completed Reading Guide with you to the next class.
• Begin Homework 1.
Monday
September 9
Sample spaces and events
Axioms of probability
Do the following before next class:
• Read §1.3 and answer the questions on the Reading Guide.
• Finish Homework 1 (due Wednesday at 4pm in the homework mailbox).
Wednesday
September 11
Counting methods
Permutations and combinations
Homework 1
due today
Do the following before next class:
• Read this article by Carol Dweck and answer the questions on the Reading Guide. Also make a conjecture about the cookie problem on the Reading Guide.
• Begin Homework 2 (due 4pm Monday).
Friday
September 13
More counting methods
Do the following before next class:
Monday
September 16
Conditional probability
Bayes' Theorem
Homework 2
due today
Do the following before next class:
• Begin Homework 3 (due 4pm Friday).
Wednesday
September 18
Independence
Do the following before next class:
Friday
September 20
Simulation of random events
Homework 3
due today
Do the following before next class:
Monday
September 23
Random variables
Discrete distributions
Do the following before next class:
Wednesday
September 25
Expected value
Variance and standard deviation
Homework 4
due today
Do the following before next class:
Friday
September 27
Binomial distribution
Do the following before next class:
Monday
September 30
Poisson 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
October 2
Review for exam
Homework 5
due today
Study for Exam 1.

Extra credit opportunity: Attend either of Dr. Eugenia Cheng's talks on Thursday October 3 (3:30pm in Tomson 280 or 7:00pm in Carleton Weitz Cinema) and answer these two questions on Moodle to earn two extra-credit homework points.

Friday
October 4
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
October 7
Poisson distribution
Do the following before next class:
Wednesday
October 9
Hypergeometric distribution
Do the following before next class:
Friday
October 11
Negative binomial distribution
Geometric distribution
Homework 6
due today
Fall break! No class Monday, October 14.
Do the following before next class:
Wednesday
October 16
Moment generating functions
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.
• Finish Homework 7 (due 4pm Friday).
Friday
October 18
Moment generating functions
Homework 7
due today
Do the following before next class:
• Read §2.8 and answer the questions on the Reading Guide.
• Begin Homework 8 (due 4pm Wednesday).
• If possible, bring a computer with R and RStudio to class on Monday.
Monday
October 21
Simulation of discrete random variables
Do the following before next class:
Wednesday
October 23
Continuous random variables
Uniform distribution
Homework 8
due today
Do the following before next class:
Friday
October 25
Expected values and moment generating functions of continuous distributions
Do the following before next class:
Monday
October 28
Normal distribution
Homework 9
due today
Do the following before next class:
Wednesday
October 30
Exponential distribution
Do the following before next class:
Friday
November 1
Gamma distribution
Homework 10
due today
Do the following before next class:
Monday
November 4
Transformations of continuous random variables
Do the following before next class:
• Re-read §3.7, focusing on Examples 3.39–3.41.
• Work on Homework 11.
Wednesday
November 6
Transformation and simulation
Do the following before next class:
Friday
November 8
Review for exam
Take-home exam problems distributed
Homework 11
due today
Complete the take-home exam problems. Bring your solutions to the exam on Monday.
Monday
November 11
Exam 2
• This exam will cover Sections 2.1 through 2.7 and 3.1 through 3.4.
• 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 in-class exam.
Do the following before next class:
Wednesday
November 13
Joint distributions
Do the following before next class:
Friday
November 15
Expected values
Covariance and correlation
Homework 12
due today
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 Wednesday).
Monday
November 18
Linear combinations of random variables
Do the following before next class:
Wednesday
November 20
Properties of linear combinations
Homework 13
due today
Do the following before next class:
Friday
November 22
Conditional distributions and expectation
Do the following before next class:
• Read §4.5.1 and §4.5.2. Answer the questions on the Reading Guide.
• Finish Homework 14 (due 4pm Monday).
• If possible, bring a computer with R to class on Monday.
Monday
November 25
Limit theorems
Homework 14
due today
Thanksgiving break! No class November 27 or 29.
Do the following before next class:
Monday
December 2
Limit theorems
Do the following before next class:
Wednesday
December 4
Transformations of random variables
Distribution function method
Do the following before next class:
• Re-read §4.6. There is no new reading guide for Wednesday.
• Finish Homework 15.
Friday
December 6
Transformations of random variables
Bivariate transformation theorem
Homework 15
due today
Do the following before next class:
Monday
December 9
Order statistics
Do the following before next class:
Wednesday
December 11
Review day
Homework 16
due today
Friday
December 13
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 December 11 and due at the final exam time on December 13. 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.