Documentation

## Bernoulli Distribution

### Overview

The Bernoulli distribution is a discrete probability distribution with the only two possible values for the random variable. Each instance of an event with a Bernoulli distribution is called a Bernoulli trial.

### Parameters

The Bernoulli distribution uses the following parameter.

ParameterDescriptionSupport
`p`Probability of success$0\le p\le 1$

### Probability Mass Function

The probability mass function (pmf) is

`$f\left(x|p\right)=\left\{\begin{array}{c}1-p\text{ },\text{ }x=0,\\ \text{ }p\text{ },\text{ }x=1\end{array}\text{\hspace{0.17em}}.$`

### Mean and Variance

The mean is

`$\text{mean}=p\text{\hspace{0.17em}}.$`

The variance is

`$\mathrm{var}=p\left(1-p\right)\text{\hspace{0.17em}}.$`

### Relationship to Other Distributions

The Bernoulli distribution is a special case of the binomial distribution, with the number of trials n = 1. The geometric distribution models the number of Bernoulli trials before the first success (or first failure).