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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.

September 8

- 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.

September 11

- 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.*

Bonus video: Paths to Math: John Urschel

- Begin Homework 2 (due Monday).
- Watch the video Four Types of Couting Problems and answer the questions embedded in the video before class on Friday.

September 15

- 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.

Bonus video: Eugenia Cheng on The Late Show

- 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.

September 20

- 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.

- 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).

September 25

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

- 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).

- 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.

September 29

- 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).
- Read the Exam 1 Information. Study for the exam.

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

- 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.

October 6

**Exam 1:**covering sections 1.1 through 2.4 in the textbook

- Watch the video The Hypergeometric Distribution and answer the questions embedded in the video. Also read §2.6.1 in the textbook.

October 9

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

- Review the problems and solutions from 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 Friday).

October 11

- Review the problems and solutions from 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 Friday).

- 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.

October 18

- 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.

- 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).

October 23

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

- 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 Wednesday).

- 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).

October 27

- 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).

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

- 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).

November 1

- Review the problems and solutions from class.
- Watch the video Transformation of a Random Variable and answer the questions in the video. Also read §3.7 in the textbook.
- Review the Exam 2 Information.
- Finish Homework 11 (due Friday).

- Review the problems and solutions from class.
- Watch the video Simulation of Continuous Random Variables and answer the questions in the video. Also read §3.8 in the textbook.
- Begin Homework 12 (due Wednesday).

November 6

Bonus video: MEET a Mathematician! - Trachette Jackson

- Review the problems and solutions from class.
- Finish Homework 12 (due Wednesday).
- Review the Exam 2 Information and study for the exam.

November 10

**Exam 2**: covering sections 2.1 through 3.4 in the textbook

- Watch the video Joint Distributions and answer the questions in the video. Also read §4.1 in the textbook.

November 13

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

- 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).

November 15

- 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).

- 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.

November 20

- Review the problems and solutions from class last Monday.
- Watch the video Conditional Distributions and answer the questions in the video. Also read §4.4 in the textbook.
- Finish Homework 14 (due Monday).
- Optionally, watch Convolutions | Why X+Y in probability is a beautiful mess by 3Blue1Brown.

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

- 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).

November 29

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

- 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).

- Review the problems and solutions from class.
- Watch the video Bivariate Transformations, Part 1 and answer the questions in the video. Also read §4.6 in the textbook.
- Begin Homework 16 (due Wednesday).

December 4

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

- Review the problems and solutions from class.
- Watch the video Bivariate Transformations, Part 2 and answer the questions in the video. Re-read §4.6 in the textbook.
- Finish Homework 16 (due Wednesday).

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

- 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!

December 8

- Review the problems and solutions from class.
- Work on Homework 17 (due Monday).
- Read the final exam information.

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

December 15

**Final Exam 9:00–11:00am**