Discrete Random Variables

This introductory course examines discrete random variables and their probability mass and cumulative distribution functions. It covers expected value, variance, binomial, hypergeometric, Poisson, and negative binomial distributions, with examples involving games of chance.

Syllabus

An Introduction to Random Variables.
Binomial Random Variables and the Binomial Distribution (part 1).
Binomial Random Variables and the Binomial Distribution (part 2).
Hypergeometric Random Variables and the Hypergeometric Distribution.
Probabilities for Discrete Random Variables.
Probability Mass Functions.
Cumulative Distribution Functions for Discrete Random Variables.
Expected Value for Discrete Random Variables.
Expected Value for a Binomial Random Variable.
Expected Value for a Hypergeometric Random Variable.
Expected Value of a Function of a Discrete Random Variable.
Variance of a Random Variable.
Variance (Discrete Example).
Poisson Distributions Basics.
Binomial Basics.
Negative Binomial Basics.
Basic Games of Chance.