Matthew L. Wright
Associate Professor, St. Olaf College

Probability Theory

Math 262 ⋅ Fall 2023

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Welcome to Probability Theory! For course info and policies, please see the syllabus. For grades, log into Moodle. If you need help or have questions, please contact Prof. Wright.

Prof. Wright's drop-in hours: typically Mon. 1–2pm, Tues. 1:30–2:30pm, Wed. 11am–noon, Thurs. 10–11am, and Fri. 9–10am in RMS 405. Check Google Calendar for up-to-date availability, or email to schedule an appointment.

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Friday
September 8
Introduction; what is probability?
probability questions Introductory Survey Homework 1
Do the following before next class:
  • Complete the Introductory Survey, if you haven't done so already.
  • Read the Syllabus.
  • From the textbook, read §1.1 and §1.2, at least through page 10, and watch the accompanying video Sample Spaces, Events, and Axioms. Answer the three questions embedded in the video before class on Monday. The first time you access videos for this course, you might need to use the "Panopto Course Videos" link on the MATH 262 Moodle page.
  • Take a look at Homework 1, which is due Wednesday.
Monday
September 11
Sample spaces and events; axioms of probability
class notes in-class solutions Sample Spaces, Events, and Axioms
Do the following before next 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
September 13
Counting methods; permutations and combinations
class notes solutions Counting Methods
Homework 1
due at 5pm

Bonus video: Paths to Math: John Urschel

Friday
September 15
More counting methods
class notes solutions Four Types of Counting Problems
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
September 18
Conditional probability; Bayes' Theorem
class notes solutions Conditional Probability
Homework 2
due at 5pm

Bonus video: Eugenia Cheng on The Late Show

Do the following before next 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 20
Independence
class notes solutions Independence
Do the following before next class:
  • Finish 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.
  • If possible, bring a computer with Mathematica or R to class on Friday.
Friday
September 22
Simulation of random events
Mathematica solutions R solutions simulation solutions 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 Wednesday).
Monday
September 25
Random variables; discrete distributions
class notes solutions Discrete Random Variables

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.
  • 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 27
Expected value, variance, and standard deviation
class notes solutions Expected Value and Standard Deviation
Homework 4
due at 5pm
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).
  • Read the Exam 1 Information. Begin reviewing what you learned from Chapter 1 in our textbook.
Friday
September 29
Binomial distribution
class notes solutions The Binomial Distribution
Do the following before next class:
Monday
October 2
Poisson distribution
class notes solutions The Poisson Distribution
Homework 5
due at 5pm

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

Do the following before next class:
  • Review the problems and solutions from 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.
Wednesday
October 4
Review day
solutions
Homework 6
(not collected)
Complete the take-home exam problems. Bring your solutions to the in-class exam on Friday.
Friday
October 6
Exam 1: covering sections 1.1 through 2.4 in the textbook
Exam 1 Information
Do the following before next class:
Monday
October 9
Hypergeometric distribution
class notes solutions The Hypergeometric Distribution

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

Do the following before next class:
Wednesday
October 11
Negative binomial and geometric distributions
class notes solutions The Negative Binomial Distribution
Do the following before next class:
Friday
October 13
Moment-generating functions
class notes solutions Moment Generating Functions, part 1
Homework 7
due at 5pm
Have a great Fall Break! No class October 16.
Do the following before next class:
  • Review the problems and solutions from class on Friday.
  • Watch the video Moment Generating Functions, Part 2 and answer the questions in the video. Re-read §2.7 in the textbook.
  • Begin Homework 8 (due Friday).
  • If possible, bring a computer with Mathematica to class on Wednesday.
Wednesday
October 18
Moment-generating functions
class notes mathematica solutions Moment Generating Functions, part 2
Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video Simulation of Discrete Random Variables and answer the questions in the video. Also read §2.8 in the textbook.
  • Finish Homework 8 (due Friday).
  • Bring a computer with Mathematica or R to class on Friday.
Friday
October 20
Simulation of discrete random variables
class demo class demo queue simulation queue simulation solutions Simulation of Discrete Random Variables
Homework 8
due at 5pm
Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video Continuous Random Variables and answer the questions in the video. Also read §3.1 in the textbook.
  • Begin Homework 9 (due Wednesday).
Monday
October 23
Continuous random variables; uniform distribution
class notes solutions Continuous Random Variables

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:
Wednesday
October 25
Expected values of continuous distributions
class demo class notes solutions Expected Values of Continuous Random Variables
Homework 9
due at 5pm
Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video The Normal Distribution and answer the questions in the video. Also read §3.3 in the textbook.
  • Begin Homework 10 (due Monday).
Friday
October 27
Normal distribution
class notes solutions The Normal Distribution
Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video The Exponential Distribution and answer the questions in the video. Also read §3.4.1 in the textbook.
  • Complete Homework 10 (due Monday).
Monday
October 30
Exponential distribution
class notes solutions The Exponential Distribution
Homework 10
due at 5pm

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video The Gamma Distribution and answer the questions in the video. Also read §3.4.2 in the textbook.
  • Begin Homework 11 (due Friday).
Wednesday
November 1
Gamma distribution
class notes solutions The Gamma Distribution
Do the following before next class:
Friday
November 3
Transformations of continuous random variables
class notes solutions Transformation of a Random Variable
Homework 11
due at 5pm
Do the following before next class:
Monday
November 6
Simulation of continuous random variables
Mathematica simulation R simulation class notes solutions Simulation of Continuous Random Variables

Bonus video: MEET a Mathematician! - Trachette Jackson

Do the following before next class:
Wednesday
November 8
Review day
solutions
Homework 12
due at 5pm
Complete the take-home exam problems. Bring your solutions to the in-class exam on Friday.
Friday
November 10
Exam 2: covering sections 2.1 through 3.4 in the textbook
Exam 2 Information
Do the following before next class:
  • Watch the video Joint Distributions and answer the questions in the video. Also read §4.1 in the textbook.
Monday
November 13
Joint distributions
class notes solutions Joint Distributions

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

Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video Covariance and Correlation and answer the questions in the video. Also read §4.2 in the textbook.
  • Begin Homework 13 (due Friday).
Wednesday
November 15
Expected values, covariance, and correlation
class notes solutions Covariance and Correlation
Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video Linear Combinations, Part 1 and answer the questions in the video. Also read from the beginning of §4.3 up to the §4.3.1 heading.
  • Finish Homework 13 (due Friday).
Friday
November 17
Linear combinations of random variables
class notes problems solutions Linear Combinations, Part 1
Homework 13
due at 5pm
Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video Linear Combinations, Part 2 and answer the questions in the video. Also read the rest of §4.3 in the textbook.
  • Begin Homework 14. This is due Monday, Nov. 27, but it's recommended to complete as much of it as possible before Thanksgiving break.
Monday
November 20
Properties of linear combinations
class notes problems solutions Linear Combinations, Part 2

Bonus: Susan D'Agostino book and interview

Have a great Thanksgiving! No class November 22 or 24.
Do the following before next class:
Monday
November 27
Conditional distributions and expectation
class notes problems solutions Conditional Distributions
Homework 14
due at 5pm

Bonus video: Francis Su — Mathematics for Human Flourishing short version and long version

Math faculty candidate presentation: Monday, November 27, 3:30pm in RNS 310; extra credit opportunity

Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video The Central Limit Theorem and answer the questions in the video. Also read §4.5 through the end of §4.5.3.
  • Begin Homework 15 (due Friday).
Wednesday
November 29
Limit theorems
Mathematica demo class notes problems solutions The Central Limit Theorem

Math faculty candidate presentation: Wednesday, November 29, 3:30pm in RNS 310; extra credit opportunity

Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video The Law of Large Numbers and answer the questions in the video. Also read §4.5.4 in the textbook.
  • Finish Homework 15 (due Friday).
Friday
December 1
Limit theorems
Mathematica class notes problems The Law of Large Numbers
Homework 15
due at 5pm
Do the following before next class:
Monday
December 4
Transformations (cdf method)
problems solutions Bivariate Transformations, Part 1

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

Math faculty candidate presentation: Monday, December 4, 3:30pm in RNS 310; extra credit opportunity

Do the following before next class:
Wednesday
December 6
Bivariate tranformation theorem
class notes problems solutions Bivariate Transformations, Part 2
Homework 16
due at 5pm

Math faculty candidate presentation: Thursday, December 7, 3:30pm in RNS 310; extra credit opportunity

Do the following before next class:
  • Review the problems and solutions from class.
  • Watch the video Order Statistics and answer the questions in the video. Also read §4.9 in the textbook.
  • Begin Homework 17 (due Monday).

See Bacterial Growth: Not So Simple for an application of iid random variables, the memoryless property, simulation, and more!

Friday
December 8
Order statistics
class notes problems solutions Order Statistics
Do the following before next class:
Monday
December 11
Review day
problems solutions
Homework 17
due at 5pm

Math faculty candidate presentation: Monday, December 11, 3:30pm in RNS 310; extra credit opportunity

Complete the take-home exam problems. Bring your solutions to the in-class exam on Friday. Study for the in-class exam.
Friday
December 15
Final Exam 9:00–11:00am
Final Exam Information