## 1.11 Discrete Probability Distributions: Example Problems (Binomial, Poisson, Hypergeometric, Geometric)

I work through a few probability examples based on some common discrete probability distributions (binomial, Poisson, hypergeometric, geometric — but not necessarily in this order). I assume that you’ve been previously introduced to these distributions (although this isn’t necessary for the geometric problem, as the probability is easily calculated from basic probability rules). Students sometimes … Read more

## 1.12 The Relationship Between the Binomial and Poisson Distributions

A look at the relationship between the binomial and Poisson distributions (roughly, that the Poisson distribution approximates the binomial for large n and small p). I work through some calculations in an example, showing that the approximate probability from the Poisson can be quite close to the exact probability from the binomial distribution. (The example … Read more

## 1.13 Proof that the Binomial Distribution tends to the Poisson Distribution

A proof that as n tends to infinity and p tends to 0 while np remains constant, the binomial distribution tends to the Poisson distribution.

## 1.13 An Introduction to the Multinomial Distribution

An introduction to the multinomial distribution, a common discrete probability distribution. I discuss the basics of the multinomial distribution and work through two examples of probability calculations. For comparison purposes, I finish off with a quick example of a multivariate hypergeometric probability calculation.

## 1.14 An Introduction to the Geometric Distribution

An introduction to the geometric distribution. I discuss the underlying assumptions that result in a geometric distribution, the formula, and the mean and variance of the distribution. I work through an example of the calculations and then briefly discuss the cumulative distribution function.

## 1.15 An Introduction to the Negative Binomial Distribution

An introduction to the negative binomial distribution, a common discrete probability distribution. In this video I define the negative binomial distribution to be the distribution of the number of *trials* needed to obtain r successes in repeated independent Bernoulli trials. Different sources define it in different ways (the distribution of the number of *failures* before … Read more

## 1.16 Introduction to the Multinomial Distribution

An introduction to the multinomial distribution, a common discrete probability distribution. I discuss the basics of the multinomial distribution and work through two examples of probability calculations. For comparison purposes, I finish off with a quick example of a multivariate hypergeometric probability calculation.

## 1.17 Poisson or Not? (When does a random variable have a Poisson distribution?)

A not-too-technical look at the conditions required for a random variable to have a Poisson distribution. It can be difficult to determine whether a random variable actually has a Poisson distribution, so here I look at a few examples and some visual illustrations that may help. There are no probability calculations carried out in this … Read more

## 1.18 Overview of Some Discrete Probability Distributions (Binomial,Geometric,Hypergeometric,Poisson,NegB)

A brief overview of some common discrete probability distributions (Bernoulli, Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson). I discuss when these distributions arise and the relationships between them. I do not do any calculations in this video, or discuss the probability mass functions or other characteristics of the distributions. This video is simply an overview of … Read more

## 2.1 An Introduction to Continuous Probability Distributions

An introduction to continuous random variables and continuous probability distributions. I briefly discuss the probability density function (pdf), the properties that all pdfs share, and the notion that for continuous random variables probabilities are areas under the curve.