MATH 230: Probability - Schedule

Class outline:

A crucial part of learning probability is via hands-on problem solving. Here is how time in class will be allocated.

We will spend the first 5-10 minutes of class reviewing important concepts and materials from the previous day. This is a good opportunity for you to raise any lingering questions you might have.
We then take a short quiz that is all T/F and Multiple Choice questions. These will mainly be conceptual questions as well as simple problems that are meant consolidate your understanding of the material and to let you assess your own understanding of the materials.
Right after the quiz, we will go through the solutions and address any questions you might have. This is another great opportunity for you to ask questions to clarify any concept, theorem, formulae that you are still unsure about.
We will go through the lecture topic/examples for class that day.
We will solve some related problems.
I will highlight the most important part of the reading that night that you should focus on.

Some Tips

Do not fall behind. The material, especially at the beginning of the course, could be deceptively easy, since most of us have some intuitive understanding of what probability is already. However, the course will quickly ramp up in pace and difficulty, especially given our condensed summer schedule.

The homework problems that I assign are the absolute bare minimum. You are encouraged to solve more problems in the textbook if time and interest allows. Feel free to come to the instructor with any questions.

Lecture Schedule

We will follow Pitman's textbook closely throughout.

Date	Topic	Reading	Assignments
5-11 (Wed)	Introductions and Logistics. Big Picture. Foundations and Interpretations of Probability.	Pitman 1.1, 1.2	First day of class. No quiz or homework problems assigned.
5-12 (Thu)	Distributions. Operations on Events.	Pitman 1.3	HW1: Section 1.3 Questions 5, 14
5-13 (Fri)	Conditional Probability. Independence.	Pitman 1.4	HW1: Section 1.4 Questions 4, 12
5-16 (Mon)	Combinatorics and Counting. Problem Solving Strategies.	Blitzstein and Hwang 1.4, (Optionally, read Blitzstein and Hwang 1.5 as well)	HW1 due today at noon. HW2: Pitman Section 1.4 Questions 6, 8
5-17 (Tue)	Bayes Rule. Problem Solving with Bayes Rule.	Pitman 1.5	HW2: Section 1.5 Question 5
5-18 (Wed)	Sequence of Events. Problem Solving Based on Conditional Probability.	Pitman 1.6	HW2: Section 1.6 Questions 3, 6
5-19 (Thu)	Review Session and Problem Solving.	Pitman Chapter 1 Review	No HW assigned for today
5-20 (Fri)	The Binomial Distribution. Binomial Theorem.	Pitman 2.1	HW2: Section 2.1 Questions 1, 7
5-23 (Mon)	Normal and Poisson Approximations.	Pitman 2.2, 2.4	HW2 due today at noon. HW3: Section 2.2 Question 12 Section 2.4 Question 5
5-24 (Tue)	Introduction to Other Discrete Distributions. Introduction to Random Sampling.	Pitman 2.5	HW3: Section 2.5 Questions 7, 8
5-25 (Wed)	Midterm Review and Q&A.
5-26 (Thu)	Midterm
5-27 (Fri)	Random variables.	Pitman 3.1	HW3: Section 3.1 Question 15
5-30 (Mon)	Memorial Day. No class held.		Homework due the next day due to Memorial Day.
5-31 (Tue)	Expectations. Variance. Moments.	Pitman 3.2, 3.3	No quiz today. HW3 due at noon today. HW4: Section 3.2 Question 8 Section 3.3 Question 3
6-01 (Wed)	Continuous Distributions. Density Functions. Revisiting the Gaussian Distribution.	Pitman 4.1	HW4: Section 4.1 Questions 2, 4
6-02 (Thu)	Exponential and Gamma distributions	Pitman 4.2	HW4: Section 4.2 Question 1
6-03 (Fri)	Change of variables.	Pitman 4.4	HW4: Section 4.4 Questions 1, 5
6-06 (Mon)	Cumulative Distribution Function. Inverse CDF Method.	Pitman 4.5	HW4 due at noon today. HW5: Section 4.5 Questions 1,5
6-07 (Tue)	Uniform Distributions. Joint Densities.	Pitman 5.1, Pitman 5.2	HW5: Section 5.1 Question 4 Section 5.2 Question 10
6-08 (Wed)	Review and Catch Up Day. Review, Problem Solving and Q+A.
6-09 (Thu)	Conditional Distributions	Pitman 6.1, Pitman 6.3	HW5: Section 6.1 Question 4 Section 6.3 Question 4
6-10 (Fri)	Conditional Expectations	Pitman 6.2	HW5: Section 6.2 Question 18
6-13 (Mon)	Covariance and Correlation	Pitman 6.4	HW5 due at noon today. HW6: Section 6.4 Question 15 parts a, b and c.
6-14 (Tue)	Bivariate Normal Distribution	Pitman 6.5	HW6: Section 6.5 Questions 4
6-15 (Wed)	Some Basic Inequalities (Markov, Chebyschev). Weak and Strong Laws of Large Numbers.	Blitzstein-Hwang 10.1 and Blitzstein-Hwang 10.2	HW6: Blitzstein Hwang 10.7 Question 21
6-16 (Thu)	Cont. LLNs. Central Limit Theorem.	Blitzstein-Hwang 10.3	HW6: Blitzstein Hwang 10.7 Question 22
6-17 (Fri)	Last Day of Class. Final Review and Q&A.
6-20 (Mon)	Juneteenth Holiday. No Class.		HW6 due at noon today.
6-21 (Tue)	Reading Day. No Class.
6-22 (Wed)	Final Exam

Acknowledgements

I am indebted to Henry Kirveslahti and Sarah Schott for helpful advice and for generously sharing materials. Much of the course design and materials are heavily influenced by and borrowed from them.