## MTH 201 - Class Notes and Practice Problems

### Class Notes

Sep 1 - Introduction
Sep 1 - Sets
Sep 3, 8 - Counting and Finitely Many Equally Likely Outcomes
Sep 10 - Infinitely Many Outcomes
Sep 15 - Consequences of Probability Axioms
Sep 15 - Random Variables, Discrete Random Variables
Sep 17 - Probability Distributions of Random Variables
Sep 17 - Conditional Probability
Sep 22 - Multiplication Rule
Sep 22 - Law of Total Probability
Sep 24 - Bayes
Sep 24, 29 - Independence
Sep 29 - Independent Trials
Oct 1 - Cumulative Distribution Function
Oct 8 - Expectation and Variance
Oct 13 - Normal Distribution
Oct 15 - Normal Approximation to Binomial
Oct 20 - Poisson Distribution
Oct 22 - Exponential Distribution
Oct 22 - Law of Large Numbers
Oct 27 - Moment Generating Functions
Oct 29 - Joint Distributions
Oct 29 - Joint Distribution Examples
Nov 3 - Multinomial Distribution, Joint CDF
Nov 5 - Independence and Joint Distributions
Nov 10 - Expectation with Multiple Random Variables
Nov 10 - Linearity of Expectation
Nov 10 - Variance and Covariance
Nov 12 - Variance of a Sum, Uncorrelated
Nov 12 - Independence and Expectation and Variance
Nov 12 - Correlation
Nov 17 - Sums of Random Variables
Nov 17 - Moment Generating Function of a Sum of Independent Variables
Nov 17 - Negative Binomial Distribution
Nov 19, 24 - Poisson Process
Nov 24 - Poisson Process Example
Nov 24, Dec 1 - Probabilistic Inequalities, Law of Large Numbers
Dec 1 - Central Limit Theorem
Dec 1, 3 - Conditional Distributions - Discrete
Dec 3 - Conditional Distributions - Jointly Continuous
Remark: Some of these notes were graciously provided by a student in the class. These are a bit faint, but still readable. I don't have my own set of handwritten notes for these classes because I wasn't using the projector.

### Practice Problems and Solutions

These problems and solutions are from a **different** but similar course taught by Joe Blitzstein at Harvard using a **different** but similar textbook.

Some topics in our course are covered differently or not at all in the Harvard course. Some topics in the Harvard course are covered differently or not at all in our course.

These problems and solutions are **not** representative of what you are expected to know for the exams, but they may be useful to you.

Practice Problems and Solutions