## 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