## 1.1 An Introduction to Discrete Random Variables and Discrete Probability Distributions

An introduction to discrete random variables and discrete probability distributions. A few examples of discrete and continuous random variables are discussed. This is an updated and revised version of an earlier video. Those looking for my original Intro to Discrete … Watch the Video

## 1.2 The Expected Value and Variance of Discrete Random Variables

An introduction to the concept of the expected value of a discrete random variable. I also look at the variance of a discrete random variable. The formulas are introduced, explained, and an example is worked through. This is an updated … Watch the Video

## 1.3 Introduction to the Bernoulli Distribution

An introduction to the Bernoulli distribution, a common discrete probability distribution.

## 1.4 The Bernoulli Distribution: Deriving the Mean and Variance

I derive the mean and variance of the Bernoulli distribution.

## 1.5 An Introduction to the Binomial Distribution

An introduction to the binomial distribution. I discuss the conditions required for a random variable to have a binomial distribution, discuss the binomial probability mass function and the mean and variance, and look at two examples involving probability calculations. The … Watch the Video

## 1.6 Binomial/Not Binomial: Some Examples

I work through a few word problems. For some the random variable has a binomial distribution, for others it does not. I hope to illustrate when the binomial distribution is appropriate, and when it is not. This video is inspired … Watch the Video

## 1.7 The Binomial Distribution: Mathematically Deriving the Mean and Variance

I derive the mean and variance of the binomial distribution. I do this in two ways. First, I assume that we know the mean and variance of the Bernoulli distribution, and that a binomial random variable is the sum of … Watch the Video

## 1.8 An Introduction to the Hypergeometric Distribution

An introduction to the hypergeometric distribution. I briefly discuss the difference between sampling with replacement and sampling without replacement. I describe the conditions required for the hypergeometric distribution to hold, discuss the formula, and work through 2 simple examples. I … Watch the Video

## 1.9 An Introduction to the Poisson Distribution

A brief introduction to the Poisson distribution. I discuss the conditions required for the Poisson distribution to hold, discuss the formula, and look at a simple example. I end off with a brief discussion of the relationship between the binomial … Watch the Video

## 1.10 The Poisson Distribution: Mathematically Deriving the Mean and Variance

I derive the mean and variance of the Poisson distribution.