Matthew L. Wright
Assistant Professor, St. Olaf College

Probability Theory

Math 262 ⋅ Spring 2022

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Wednesday
February 9
Introduction; what is probability?
Do the following before next class:
Friday
February 11
Sample spaces and events; axioms of probability
Do the following before next class:
  • Complete Homework 1 (due Monday).
  • Read §1.3 in the textbook, and watch the accompanying video Counting Methods. Answer the three questions embedded in the video before class on Monday.
Monday
February 14
Counting methods; permutations and combinations
Homework 1
due at 5pm

Bonus video: John Urschel-NFL Math Whiz

Do the following before next class:
Wednesday
February 16
Do the following before next class:
  • Finish Homework 2 (due Friday).
  • Watch the video Conditional Probability and answer the questions embedded in the video before coming to class on Friday. Also read the examples in §1.4 in the textbook.
Friday
February 18
Conditional probability; Bayes' Theorem
Homework 2
due at 5pm
Do the following before next class:
  • Begin Homework 3 (due Wednesday).
  • Watch the video Independence and answer the questions embedded in the video before coming to class on Monday. Also read §1.5 in the textbook.
Monday
February 21

Bonus video: Eugenia Cheng on The Late Show

Do the following before next class:
  • Finish Homework 3 (due Wednesday).
  • Watch the video Simulation of Random Events and answer the questions embedded in the video before coming to class on Wednesday. Also read §1.6 in the textbook.
  • If possible, bring a computer with Mathematica or R to class on Wednesday.
Wednesday
February 23
Simulation of random events
Homework 3
due at 5pm
Do the following before next class:
  • 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 Monday).
Friday
February 25
Random variables; discrete distributions
Do the following before next class:
Monday
February 28
Expected value, variance, and standard deviation
Homework 4
due at 5pm

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:
  • 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 Friday).
Wednesday
March 2
Do the following before next class:
Friday
March 4
Homework 5
due at 5pm
Do the following before next class:
  • Complete Homework 6. This homework will not be collected, but it is important for your own practice as you prepare for Exam 1.
  • Review the Exam 1 Information.
Monday
March 7
Review day
Homework 6
(not collected)

Bonus video: Hannah Fry — Beautiful equations: how insects walk on water and galaxies form

Complete the take-home exam problems. Bring your solutions to the in-class exam on Wednesday.
Wednesday
March 9
Exam 1: covering sections 1.1 through 2.4 in the textbook
Do the following before next class:
Friday
March 11
Do the following before next class:
Monday
March 14
Negative binomial and geometric distributions

Bonus videos: Satyan Devadoss — Blue Collar Mathematics and Mage Merlin's Unsolved Mathematical Mysteries

Do the following before next class:
Wednesday
March 16
Homework 7
due at 5pm
Do the following before next class:
Friday
March 18
Do the following before next class:
Monday
March 21
Homework 8
due at 5pm

Bonus video: Moon Duchin: "Political Geometry"

Do the following before next class:
Wednesday
March 23
Continuous random variables; uniform distribution
Do the following before next class:
Friday
March 25
Expected values of continuous distributions
Homework 9
due at 5pm
Have a great spring break! No class March 28 – April 1.
Do the following before next class:

Bonus video: Francis Su — Mathematics for Human Flourishing

Do the following before next class:
Wednesday
April 6
Homework 10
due at 5pm
Do the following before next class:
Do the following before next class:
Monday
April 11
Review day
Homework 11
due at 5pm

Bonus video Interview with Karen Uhlenbeck and article Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize

Complete the take-home exam problems. Bring your solutions to the in-class exam on Wednesday.
Wednesday
April 13
Exam 2: covering sections 2.1 through 3.4 in the textbook
Do the following before next class:
Friday
April 15
Transformations of continuous random variables
Do the following before next class:

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

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 Wednesday).
Wednesday
April 20
Homework 12
due at 5pm
Do the following before next class:
Friday
April 22
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 Monday).
Monday
April 25
Linear combinations of random variables
Homework 13
due at 5pm

Bonus video: MEET a Mathematician! - Trachette Jackson

Do the following before next class:
Wednesday
April 27
Do the following before next class:
Friday
April 29
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 Wednesday).

Bonus: Why is Mathematics Useful — Robert Ghrist, and Applied Dynamical Systems Vol. 1

Do the following before next class:
Wednesday
May 4
Homework 15
due at 5pm
Do the following before next class:
Friday
May 6
Do the following before next class:
Monday
May 9
Bivariate tranformation theorem
Homework 16
due at 5pm

Bonus: Susan D'Agostino book and interview

Do the following before next class:
  • Watch the video Order Statistics and answer the questions in the video before class on Monday. Also read §4.9 in the textbook.
  • Begin Homework 17 (due next Monday).
Wednesday
May 11
Do the following before next class:
Friday
May 13
Probability paradoxes
Do the following before next class:
Monday
May 16
Review day
Homework 17
due at 5pm

Bonus: Living Proof: Stories of Resilience Along the Mathematical Journey

Complete the take-home exam problems. Bring your solutions to the in-class exam on Friday. Study for the in-class exam.
Friday
May 20
Final Exam 9:00–11:00am