1. Discrete Probability Distributions

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

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

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.

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.

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