## Binomial, Poisson, and Multinomial Distributions

First, we will talk about binomial probabilities, how to compute their cumulatives, and the mean and standard deviation. Then, we will introduce the Poisson probability formula, define multinomial outcomes, and discuss how to compute probabilities by using the multinomial distribution.

##### Learning Objectives

- Define multinomial outcomes
- Compute probabilities using the multinomial distribution

where

is the number of times outcome 1 occurs,

is the number of times outcome 2 occurs,

is the number of times outcome 3 occurs,

is the probability of outcome 1

For the chess example,

Note that the binomial distribution is a special case of the multinomial when .