Discrete Random Variables

Overview

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Explore the fundamental concepts of discrete random variables in this comprehensive lecture. Delve into an introduction to random variables before focusing on binomial and hypergeometric distributions. Learn about probability mass functions, cumulative distribution functions, and how to calculate probabilities for discrete random variables. Understand the concepts of expected value and variance, with specific examples for binomial and hypergeometric random variables. Examine Poisson, binomial, and negative binomial distributions, and apply these concepts to basic games of chance. Gain a solid foundation in probability theory and its practical applications through this in-depth exploration of discrete random variables.

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.