Matthew L. Wright
Assistant Professor, St. Olaf College

# Probability Theory

## Math 262 ⋅ Fall 2020

Top
Today
Bottom
Friday
August 21
Introduction; what is probability?
Do the following before next class:
Monday
August 24
Sample spaces and events; axioms of probability
Do the following before next class:
• Review the solutions to the problems from class.
• Complete Homework 1 (due Wednesday).
• Read §1.3 in the textbook, and watch the accompanying video Counting Methods. Answer the three questions embedded in the video before class on Wednesday.
Wednesday
August 26
Counting methods; permutations and combinations
Homework 1
due at 5pm

Bonus video: John Urschel-NFL Math Whiz

Do the following before next class:
Friday
August 28
More counting methods
Do the following before next class:
• Review the solutions to the problems from class.
• Finish Homework 2 (due Monday).
• Watch the video Conditional Probability and answer the questions embedded in the video before coming to class on Monday. Also read the examples in §1.4 in the textbook.
Monday
August 31
Conditional probability; Bayes' Theorem
Homework 2
due at 5pm
Do the following before next class:
• Review the solutions to the problems from class.
• Begin Homework 3 (due Friday).
• Watch the video Independence and answer the questions embedded in the video before coming to class on Wednesday. Also read §1.5 in the textbook.
Wednesday
September 2
Independence
Do the following before next class:
• Review the solutions to the problems from class.
• Begin Homework 3 (due Friday).
• Watch the video Simulation of Random Events and answer the questions embedded in the video before coming to class on Friday. Also read §1.6 in the textbook.
• On Friday, we meet in RNS 410. Wear your face mask, and bring your computer with R or Mathematica.
Friday
September 4
Simulation of random events
Meet in RNS 410 — masks required!
Homework 3
due at 5pm
Do the following before next class:
• Please complete the Week 3 Survey. Answers are voluntary and anonymous.
• Watch the video Discrete Random Variables and answer the questions embedded in the video before coming to class on Monday. Also read §2.1 and §2.2 in the textbook.
• Begin Homework 4 (due Wednesday).
Monday
September 7
Random variables; discrete distributions
Do the following before next class:
• Please complete the Week 3 Survey, if you haven't done so already. Answers are voluntary and anonymous.
• Watch the video Expected Value and Standard Deviation and answer the questions embedded in the video before coming to class on Wednesday. Also read §2.3 in the textbook.
• Finish Homework 4 (due Wednesday).
Wednesday
September 9
Expected value, variance, and standard deviation
Homework 4
due at 5pm

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

Do the following before next class:
• Review the solutions from the problems in class, especially those involving Chebyshev's Inequality.
• Watch the video The Binomial Distribution and answer the questions embedded in the video before coming to class on Friday. Also read §2.4 in the textbook.
• Begin Homework 5 (due Monday).
Friday
September 11
Binomial distribution
Do the following before next class:
• Review the solutions from the problems in class.
• Watch the video The Poisson Distribution and answer the questions embedded in the video before coming to class on Monday. Also read §2.5 in the textbook.
• Finish Homework 5 (due Monday).
• Take a look at Homework 6 (due Wednesday).
Monday
September 14
Poisson distribution
Homework 5
due at 5pm
Do the following before next class:
Wednesday
September 16
Review day
Homework 6
due at 5pm

Bonus video: Moon Duchin: "Political Geometry"

Work on Exam 1. Complete it before class on Monday. You may either hand in your exam at class on Monday, or submit your work electronically using this Moodle assignment link.
Friday
September 18
Exam 1: take-home, covering sections 1.1 through 2.4 in the textbook
Do the following before next class:
Monday
September 21
Hypergeometric distribution
Do the following before next class:
• Review the solutions to the problems from class on Monday. (See notes and solutions above.)
• Watch the video The Negative Binomial Distribution and answer the questions embedded in the video. Also read §2.6.2 in the textbook.
• Begin Homework 7 (due Friday).
Wednesday
September 23
Negative binomial and geometric distributions

Bonus: video How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg and article The Psychology of Statistics by Jordan Ellenberg

Do the following before next class:
Friday
September 25
Moment-generating functions
Homework 7
due at 5pm
Do the following before next class:
Monday
September 28
Moment-generating functions
Do the following before next class:
Wednesday
September 30
Simulation of discrete random variables
Homework 8
due at 5pm
Do the following before next class:
Friday
October 2
Continuous random variables; uniform distribution
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Monday
October 5
Expected values of continuous distributions
Homework 9
due at 5pm
Do the following before next class:
Wednesday
October 7
Normal distribution
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Friday
October 9
Exponential distribution
Homework 10
due at 5pm
Do the following before next class:
Monday
October 12
Gamma distribution

Extra credit opportunity: Attend one or more student presentations at the Northfield Undergraduate Mathematics Symposium (NUMS) on Tuesday, Oct. 13, 3:30-7:00pm. See here for details.

Do the following before next class:
Wednesday
October 14
Review day
Homework 11
due at 5pm

Extra credit opportunity: attend Explore MSCS on Thursday, Oct. 15, 4:00–5:00pm to earn 2 extra-credit points for your homework grade.

Work on Exam 2. Complete it before class on Monday. You may either hand in your exam at class on Monday, or submit your work electronically on Moodle.
Friday
October 16
Exam 2: take-home, covering sections 2.1 through 3.4 in the textbook
Do the following before next class:
Monday
October 19
Transformations of continuous random variables
Do the following before next class:
Wednesday
October 21
Simulation of continuous random variables

Bonus video: Francis Su — Mathematics for Human Flourishing

Do the following before next class:
• Watch the video Joint Distributions and answer the questions in the video before class on Friday. Also read §4.1 in the textbook.
• Finish Homework 12 (due Friday).
Friday
October 23
Joint distributions
Homework 12
due at 5pm
Do the following before next class:
Monday
October 26
Expected values, covariance, and correlation
Do the following before next class:
• Watch the video Linear Combinations, Part 1 and answer the questions in the video before class on Wednesday. Also read from the beginning of §4.3 up to the §4.3.1 heading.
• Finish Homework 13 (due Wednesday).
Wednesday
October 28
Linear combinations of random variables
Homework 13
due at 5pm
Do the following before next class:
Friday
October 30
Properties of linear combinations
Do the following before next class:
Monday
November 2
Conditional distributions and expectation
Homework 14
due at 5pm
Do the following before next class:
• Watch the video The Central Limit Theorem and answer the questions in the video before class on Wednesday. Also read §4.5 through the end of §4.5.3.
• Begin Homework 15 (due Friday).
Wednesday
November 4
Limit theorems
Do the following before next class:
Friday
November 6
Limit theorems
Homework 15
due at 5pm
Do the following before next class:
Monday
November 9
The Law of Large Numbers, then Transformations (cdf method)
Do the following before next class:
Wednesday
November 11
Bivariate tranformation theorem
Homework 16
due at 5pm
Do the following before next class:
• Watch the video Order Statistics and answer the questions in the video before class on Friday. Also read §4.9 in the textbook.
• Begin Homework 17 (due Monday).
Friday
November 13
Order statistics
Do the following before next class:
Monday
November 16
Homework 17
due at 5pm
We've made it to the end of the semester! A few last things to do:
Thursday
November 19
Final exam due at 4:00pm