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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 office hours: Mon. 12:45–2:00pm in RNS 160R, Tues. 10–11am on Zoom, Wed. 3:15–4:15 in RMS 405, Thurs. 10–11am in RMS 405, Fri. 12:45–2:00pm in RNS 160R, and other times by appointment
Help sessions: Mon. and Thurs. 7–8pm in Tomson 186
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Wednesday
February 9
February 9
Introduction; what is probability?
Do the following before next class:
- Complete the Introductory Survey, if you haven't done so already.
- Read the Syllabus and complete the Syllabus Quiz (on Moodle).
- 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 Friday.
- Take a look at Homework 1, which is due Monday.
Friday
February 11
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.
Bonus video: John Urschel-NFL Math Whiz
Do the following before next class:
- Begin Homework 2 (due Friday).
- Watch the video Four Types of Couting Problems and answer the questions embedded in the video before class on Wednesday.
Wednesday
February 16
February 16
More counting methods
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.
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
February 21
Independence
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.
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
February 25
Random variables; discrete distributions
Do the following before next 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 Monday).
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
March 2
Binomial distribution
Do the following before next 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 Friday).
- Read the Exam 1 Information.
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.
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
March 9
Exam 1: covering sections 1.1 through 2.4 in the textbook
Do the following before next class:
- Watch the video The Hypergeometric Distribution and answer the questions embedded in the video. Also read §2.6.1 in the textbook.
Friday
March 11
March 11
Hypergeometric distribution
Do the following before next class:
- 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 Wednesday).
Monday
March 14
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:
- Watch the video Moment Generating Functions, Part 1 and answer the questions in the video. Also read §2.7 in the textbook.
- Finish Homework 7 (due Wednesday).
Do the following before next class:
- 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 Monday).
- If possible, bring a computer with Mathematica to class on Friday.
Friday
March 18
March 18
Moment-generating functions
Do the following before next 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 Monday).
- Bring a computer with Mathematica or R to class on Monday.
Bonus video: Moon Duchin: "Political Geometry"
Do the following before next 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 Friday).
Wednesday
March 23
March 23
Continuous random variables; uniform distribution
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.
- Finish Homework 9 (due Friday).
Have a great spring break! No class March 28 – April 1.
Do the following before next class:
- Watch the video The Normal Distribution and answer the questions in the video. Also read §3.3 in the textbook.
Monday
April 4
April 4
Normal distribution
Bonus video: Francis Su — Mathematics for Human Flourishing
Do the following before next 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 Wednesday).
Do the following before next 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 Monday).
Friday
April 8
April 8
Gamma distribution
Do the following before next class:
- Review the Exam 2 Information.
- Finish Homework 11 (due Monday).
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
April 13
Exam 2: covering sections 2.1 through 3.4 in the textbook
Do the following before next class:
- Watch the video Transformation of a Random Varible. Also read §3.7 in the textbook.
Friday
April 15
April 15
Transformations of continuous random variables
Do the following before next class:
- Watch the video Simulation of Continuous Random Variables and answer the questions in the video before class on Wednesday. Also read §3.8 in the textbook.
- Begin Homework 12 (due Wednesday).
Monday
April 18
April 18
Simulation of continuous random variables
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).
Do the following before next class:
- Watch the video Covariance and Correlation and answer the questions in the video before class on Monday. Also read §4.2 in the textbook.
- Begin Homework 13 (due Monday).
Friday
April 22
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).
Bonus video: MEET a Mathematician! - Trachette Jackson
Do the following before next class:
- 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.
- Begin Homework 14 (due Friday).
Wednesday
April 27
April 27
Properties of linear combinations
Do the following before next class:
- Watch the video Conditional Distributions and answer the questions in the video before class on Monday. Also read §4.4 in the textbook.
- Finish Homework 14 (due Friday).
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).
Monday
May 2
May 2
Limit theorems
Bonus: Why is Mathematics Useful — Robert Ghrist, and Applied Dynamical Systems Vol. 1
Do the following before next 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.
- Finish Homework 15 (due Wednesday).
Do the following before next 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.
- Begin Homework 16 (due Monday).
Friday
May 6
May 6
Transformations (cdf method)
Do the following before next class:
- 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 16 (due Monday).
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
May 11
Order statistics
Do the following before next class:
- Work on Homework 17 (due Monday).
- Read the final exam information.
Do the following before next class:
- Finish Homework 17 (due Monday).
- Read the final exam information. Study for the final exam.
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
May 20
Final Exam 9:00–11:00am
