## 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 Random Variables video can find it at: http://youtu.be/0P5WRKihQ4E

## 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 and refined version of an earlier video. Those looking for the original version can find … Read more

## 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 estimated probability of a 90 year old Canadian male surviving for one year was taken … Read more

## 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 by the many times I’ve been asked something along the lines of “I don’t understand … Read more

## 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 n independent Bernoulli random variables. I then take the more difficult approach, where we do … Read more

## 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 also discuss the relationship between the binomial distribution and the hypergeometric distribution, and a rough … Read more

## 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 distribution and the Poisson distribution.

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

I derive the mean and variance of the Poisson distribution.