Matthew L. Wright
Assistant Professor, St. Olaf College

Probability Theory

Math 262 ⋅ Fall 2022

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Thursday
September 8
What is probability? Sample Spaces and Events
Do the following before next class:
Tuesday
September 13
Axioms of Probability; Permutations and Combinations
Do the following before next class:
  • Review the solutions to the problems from class.
  • Re-read §1.3 in the textbook.
  • Watch the video Four Types of Couting Problems and answer the questions embedded in the video before class on Thursday.
  • Work on Homework 1. Try to finish the problems from §1.1 and §1.2.
Thursday
September 15
Do the following before next class:
  • Review the solutions to the problems from class.
  • Watch the video Conditional Probability and answer the questions embedded in the video before coming to class on Tuesday. Also §1.4 in the textbook, paying special attention to the examples.
  • Read §1.5 in the textbook. Watch the video Independence and answer the questions embedded in the video before coming to class on Tuesday.
  • Finish Homework 1. Write your solutions clearly and neatly. Upload your solutions to Homework 1 on Moodle.
Tuesday
September 20
Conditional Probability and Independence

Bonus video: John Urschel-NFL Math Whiz

Do the following before next class:
  • Review the solutions to the problems from class.
  • Watch the video Simulation of Random Events and answer the questions embedded in the video before coming to class on Thursday. Also read §1.6 in the textbook.
  • If possible, bring a computer with Mathematica or R to class on Thursday.
  • Begin Homework 2. This homework is due next Tuesday, but it's important to start early.
Thursday
September 22
Independence; Simulation of random events
Do the following before next class:
  • Review the solutions to the problems from class.
  • Watch the video Discrete Random Variables and answer the questions embedded in the video before coming to class on Tuesday. Also read §2.1 and §2.2 in the textbook.
  • Watch the video Expected Value and Standard Deviation and answer the questions embedded in the video before coming to class on Tuesday. Also read §2.3 in the textbook.
  • Finish Homework 2. Write your solutions clearly and neatly. Upload your solutions to Homework 2 on Moodle.
Tuesday
September 27
Random variables, discrete distributions, and expected value

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

  MSCS Tailgate Party: Wednesday, September 28, 4:30–6:30pm in Tomson 280 (masks required) and outside

Do the following before next class:
  • Review the solutions to the problems from class. Also review §2.3 in the text.
  • Watch the video The Binomial Distribution and answer the questions embedded in the video before coming to class on Thursday. Also read §2.4 in the textbook.
  • Begin Homework 3. This homework is due next Tuesday, but it's important to start early.
Thursday
September 29
Chebyshev's Inequality and the Binomial Distribution
Do the following before next class:
  • Review the solutions from the problems in class, especially those involving Chebyshev's Inequality.
  • Watch the video The Poisson Distribution and answer the questions embedded in the video before coming to class on Tuesday. Also read §2.5 in the textbook.
  • Finish Homework 3. Write your solutions clearly and neatly. Upload your solutions to Homework 3 on Moodle.
Tuesday
October 4
Binomial and Poisson Distributions

  Oct. 4: Math Across the Cannon featuring Satyan Devadoss colloquium 3:30pm at Carleton; public lecture 7pm in Viking Theater; extra credit opportunity

Do the following before next class:
  • Review the solutions to the problems from class.
  • Begin Homework 4. This homework will not be collected, but you should do it before the exam. Solutions are here.
  • Read the Exam 1 Information. Study for the exam.
Thursday
October 6
Poisson Distribution; Review

Bonus video: Eugenia Cheng on The Late Show

Do the following before next class:
  • Work on Homework 4. This homework will not be collected, but you should do it before the exam. Solutions are here.
  • Review the Exam 1 Information. Study for the exam.
Tuesday
October 11
Exam 1: covering sections 1.1 through 2.4 in the textbook
Do the following before next class:
Thursday
October 13
Enjoy fall break! No class October 18.

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:

MSCS Colloquium: "Gerrymandering and the Attainment of Impossible Electoral Results" by Prof. Steve McKelvey; Friday, October 21, 3:30pm in RNS 310

MSCS Colloquium: "Painful Regressions: Probability and Statistics in Clinical Medicine and Pain Management" by Dr. Akshar Rambachan '12 MD, MPH; Monday, October 24, 3:30pm in RNS 310

Do the following before next class:
  • Review the solutions to the problems from class.
  • Finish Homework 5. Write your solutions clearly and neatly. Upload your solutions to Homework 5 on Moodle.
  • Watch the video Simulation of Discrete Random Variables and answer the questions in the video. Optionally, read §2.8 in the textbook.
  • Watch the video Continuous Random Variables and answer the questions in the video. Also read §3.1 in the textbook.
  • If possible, bring a computer with Mathematica or R to class on Tuesday.
Tuesday
October 25
Simulation of discrete random variables; Begin continuous random variables

Bonus video: Moon Duchin: "Political Geometry" and DistrictR

Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video Expected Values of Continuous Random Variables and answer the questions in the video. Also read §3.2 in the textbook.
  • Begin Homework 6, due next Tuesday. Work on the moment-generating function problems and ask questions later this week.
Thursday
October 27
Expected values of continuous distributions
Do the following before next class:
Tuesday
November 1

Bonus: Federico Ardila on Math, Music and the Space of Possibilities

Do the following before next class:
  • Review the solutions to the problems from class.
  • Begin Homework 7. This homework will not be collected, but you should do it before the exam. Solutions are here.
  • Read the Exam 2 Information. Study for the exam.
  • Watch the video The Gamma Distribution and answer the questions in the video. Also read §3.4.2 in the textbook.
Thursday
November 3
Exponential and Gamma distributions; Review
Do the following before next class:
  • Work on Homework 7. This homework will not be collected, but you should do it before the exam. Solutions are here.
  • Read the Exam 2 Information. Study for the exam.
Tuesday
November 8
Exam 2: covering sections 2.1 through 3.3 in the textbook
Do the following before next class:
Thursday
November 10

Bonus: Susan D'Agostino book and interview

Do the following before next class:
  • Review the solutions to the problems from class.
  • Do Homework 8, which is due Tuesday. This homework is shorter than usual, but it's still wise to start early and ask questions.
  • Watch the video Joint Distributions and answer the questions in the video before class on Friday. Also read §4.1 in the textbook.
  • Watch the video Covariance and Correlation and answer the questions in the video before class on Monday. Also read §4.2 in the textbook.
Tuesday
November 15
Joint Distributions and Expected Values
Do the following before next class:
  • Review the solutions to the problems from class.
  • Begin Homework 9, which is due next Tuesday. This homework involves problems on transformations of random variables. It's important to start early and ask questions!
  • 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.
Thursday
November 17
Covariance and correlation; Linear Combinations

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

Do the following before next class:
  • Review the solutions to the problems from class.
  • Finish Homework 9, which is due Tuesday.
  • Watch the video Linear Combinations, Part 2 and answer the questions in the video before class on Friday. Also read the rest of §4.3 in the textbook.
Tuesday
November 22
Linear combinations of random variables
Have a Thanksgiving! No class November 24.

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

Do the following before next class:
  • Review the solutions to the problems from class. For another perspective on convolutions, watch But what is a convolution? by 3Blue1Brown.
  • Watch the video Conditional Distributions and answer the questions in the video before class on Monday. Also read §4.4 in the textbook.
  • 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 10, which is due on Tuesday, December 6.
Tuesday
November 29
Conditional distributions and expectation

Bonus video: Christmas Lectures 2019: How to Get Lucky — Hannah Fry

Do the following before next class:
  • Review the solutions to the problems from class.
  • Watch the video The Law of Large Numbers and answer the questions in the video before class on Friday. Also read §4.5.4 in the textbook.
  • Work on Homework 10, which is due next Tuesday.
  • If possible, bring a computer with Mathematica or R to class on Thursday.
Thursday
December 1
Do the following before next class:
  • Review the solutions to the problems from class.
  • Watch the video Bivariate Transformations, Part 1 and answer the questions in the video before class on Monday. Also read §4.6 in the textbook.
  • Watch the video Bivariate Transformations, Part 2 and answer the questions in the video before class on Wednesday. Re-read §4.6 in the textbook.
  • Finish Homework 10, which is due on Tuesday.

Bonus video: Francis Su — Mathematics for Human Flourishing

Do the following before next class:
  • Review the solutions to the problems from 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 11.
Thursday
December 8
Order statistics
Do the following before next class:
Tuesday
December 13
Review day
Complete the take-home exam problems. Bring your solutions to the in-class exam on Monday. Study for the in-class exam.
Monday
December 19
Final Exam 9:00–11:00am