Lectures

Monday, June 22

1. Read the syllabus, and complete the syllabus quiz.
2. Introduce yourself in the #introductions channel on Discord.
3. Learn about “Why Study Probability? For Statisticians”. (If you have never used Colab before, you may want to watch this introductory video first.)
4. Learn about “Probability and Counting”, then measure your understanding.
5. Learn about “The Factorial”, then measure your understanding.
6. Complete the simulation activity.

Tuesday, June 23

1. Look at the results from yesterday’s simulation.
2. Learn about “Box Models”, then measure your understanding.
3. Learn about “Sampling with Replacement”, then measure your understanding.
4. Complete the simulation activity.

Wednesday, June 24

1. Look at the results from yesterday’s simulation.
2. Learn about “Double Counting”, then measure your understanding.
3. Learn about “Conditional Probability”, then measure your understanding.
4. Learn about “Independence”, then measure your understanding.
5. Complete the simulation activity.

Thursday, June 25

1. Look at the results from yesterday’s simulation.
2. Learn about “The Law of Total Probability”, then measure your understanding.
3. Learn about “Bayes’ Theorem”, then measure your understanding.
4. Complete the simulation activity.

Friday, June 26

1. Analyze the results from yesterday’s simulation.
2. Learn about “Random Variables”, then measure your understanding.
3. Learn about “Cumulative Distribution Functions”, then measure your understanding.
4. (Optional) Work with a partner on Case Study 1 on the probability of winning in the casino game craps. If you complete it, it will replace your lowest grade on this week’s activities. The points don’t justify the time, but I hope that the case study is interesting and a good review of many concepts you have learned this week. It is due at midnight on Monday, if you want to do it.

Monday, June 29

1. Learn about “The Hypergeometric Distribution”, then measure your understanding. You should be comfortable calculating probabilities using either Python or R; you do not need to know both. I encourage you to use Python or R in Colab, like I do in the lesson, so you do not need to install any software on your own machine.
2. Complete the simulation activity.
3. (Optional) Complete Case Study 1.

Tuesday, June 30

1. Learn about “The Binomial Distribution”, then measure your understanding.
2. Follow up on yesterday’s simulation activity.
3. Complete the simulation activity.

Wednesday, July 1

1. Learn about “The Geometric Distribution”, then measure your understanding.
2. Learn about “The Negative Binomial Distribution”, then measure your understanding.
3. Complete the activity. (The activity today is not a simulation; it is more of a mental exercise.)

Thursday, July 2

1. Learn about “The Poisson Distribution”, then measure your understanding.
2. Learn about “The Poisson Process”, then measure your understanding.

Friday, July 3

1. No Class - Independence Day
2. Information about Exam 1 next Friday.

Monday, July 6

1. Learn about “Joint Distributions”, then measure your understanding.
2. Complete the simulation activity.
3. Read instructions for Exam 1, which is this Friday, July 10.

Tuesday, July 7

1. Learn about “Marginal Distributions”, then measure your understanding.
2. Learn about “Conditional Distributions”, then measure your understanding.
3. Analyze the simulation results.

Wednesday, July 8

1. Learn about “Sums of Random Variables”, then measure your understanding.
2. Fill out this form for Exam 1.

Thursday, July 9

Note: These activities are due on Friday at midnight!

1. Learn about “Expected Value”, then measure your understanding.
2. Learn about “Pascal’s Wager” and complete this activity.
3. Learn about “The St. Petersburg Paradox” and complete this activity

Friday, July 10

Exam 1

Monday, July 13

1. Learn about “LOTUS”, then measure your understanding.
2. Learn about “2D LOTUS”, then measure your understanding.
3. Complete the simulation activity.

Tuesday, July 14

1. Follow up on yesterday’s simulation.
2. Learn about “Linearity of Expectation”, then measure your understanding.
3. Learn about “The Expected Value of a Product”, then measure your understanding.

Wednesday, July 15

1. Learn about “Variance”, then measure your understanding.
2. Learn about “Covariance”, then measure your understanding.

Thursday, July 16

1. Learn about “Properties of Covariance”, then measure your understanding.
2. Complete the simulation activity

Friday, July 17

1. Learn about “The Random Walk”, then measure your understanding.
2. Review the results from yesterday’s simulation activity.
3. Learn about “The Law of Large Numbers”, then measure your understanding.
4. Turn in Case for Partial Credit for Exam 1.

Monday, July 20

1. Watch “Making Probability Mathematical”, focusing on the dartboard example at the end. The video ends around 11:20; the last 3 minutes are advertising.
2. Learn about “Continuous Random Variables”, then measure your understanding.

Tuesday, July 21

1. Learn about “The Uniform Distribution”, then measure your understanding.
2. Learn about “The Exponential Distribution”, then measure your understanding.
3. Complete the simulation activity.

Wednesday, July 22

1. Review the simulation results from yesterday. (They didn’t turn out so well; there’s a much better simulation in the lesson.)
2. Learn about “Transformations”, then measure your understanding.

Thursday, July 23

1. Review the lesson on “Expected Value”.
2. Learn about “Expected Value for Continuous Random Variables”, then measure your understanding.
3. Review the lesson on “LOTUS”.
4. Learn about “LOTUS for Continuous Random Variables”, then measure your understanding.
5. Review the lesson on “Variance”.
6. Learn about “Variance for Continuous Random Variables”, then measure your understanding.

Friday, July 24

1. Learn about “the Normal Distribution”, then measure your understanding.
2. Read instructions for Exam 2, which is next Friday, July 31.

Monday, July 27

1. Review “Joint Distributions (for Discrete Random Variables)”.
2. Learn about “Joint Continuous Distributions”, then measure your understanding.
3. Review “Marginal Distributions (for Discrete Random Variables)”.
4. Learn about “Marginal Continuous Distributions”, then measure your understanding.

Tuesday, July 28

1. Review “2D LOTUS”, “Expected Value of a Product”, and “Linearity of Expectation” for discrete random variables.
2. Learn about “Expectations of Joint Continuous Distributions”, then measure your understanding.
3. Review “Covariance” and “Properties of Covariance” for discrete random variables.
4. Learn about “Covariance of Continuous Random Variables”, then measure your understanding.
5. Tomorrow’s assignment is required to be completed in groups of 2 or 3. Find a partner (or partners), and arrange a time that you will be able to work on the assignment tomorrow. Post on Discord if you are having trouble finding a partner.

Wednesday, July 29

The activities for today are tedious but are manageable if you divide up the work. That is why I am requiring that you work in groups of 2 or 3.

1. Review “Sums of Discrete Random Variables”.
2. Learn about “Sums of Continuous Random Variables”, then measure your understanding. Essential Practice #1 is a beast, but it will make you a master at convolution. This is one where it definitely pays to work in a group, drawing it out together and dividing up the calculations.
3. Complete the Colab activity “Simulating Sums of Independent Random Variables”. Submission instructions are at the bottom of the Colab notebook.

Thursday, July 30

1. Learn about “The Central Limit Theorem”, then measure your understanding.
2. Study for Exam 2 tomorrow. Make sure you have reviewed the instructions here.

Friday, July 31

1. Exam 2 from 12 PM to 2 PM. Make sure you have reviewed the instructions here.
2. Final Project instructions

Monday, August 3

You are encouraged to, but not required to, work with a partner on the lessons for the rest of the course. This partner can be, but does not have to be, your final project partner.

1. Complete Notebook 1. The Bias of an Estimator. (Submission instructions inside.)
2. Notebook 1 should help you make progress on your final project.

Tuesday, August 4

1. Peer review Notebook 1. If someone’s answer differs from your own, and you are not sure why, please ask on the Discord server!
2. Read this textbook excerpt about how the weight of a kilogram is determined.
3. Complete Notebook 2. More on Bias. (Submission instructions inside.)

Wednesday, August 5

1. Peer review Notebook 2. If someone’s answer differs from your own, and you are not sure why, please ask on the Discord server!
2. Complete Notebook 3. Estimating the Variance.

Thursday, August 6

1. Many of you struggled with Notebook 3. Please review the solutions, especially to Questions 1, 3, and 4.
2. Complete Notebook 4. Comparing Unbiased Estimators.

Friday, August 7

1. Peer review Notebook 4.
2. Complete Notebook 5. Mean-Squared Error. (You need to submit your answer to Question 3 in this Canvas quiz.
3. Exam 2 Case for Partial Credit due.

Monday, August 10

1. Complete Notebook 6. The Maximum Likelihood Principle. (Submission instructions inside.)

Tuesday, August 11

1. Peer review Notebook 6.
2. Complete Notebook 7. The Calculus of Maximum Likelihood.
3. Notebook 6 should help you make progress on your final project.

Wednesday, August 12

1. Peer review Notebook 7.
2. Complete Notebook 8. Maximum Likelihood for Continuous Random Variables.
3. Calculate the MLEs for the two scenarios on your final project.

Thursday, August 13

1. Peer review Notebook 8.
2. Complete Notebook 9. The Idea of Confidence. Check your answers using this Canvas quiz.

Friday, August 14

1. Complete Notebook 10. Confidence Intervals in Practice.
2. You and your project partner (if applicable) should add yourselves to one of the Final Project Groups on Canvas.
3. Fill out project survey.
4. Work on your final project. Note that your final project materials should be submitted on Canvas before Friday, August 21 at 12 PM.

Friday, August 21

Final Project Presentation Session 4-5 PM