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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
pProbability of success0p1

Probability Mass Function

The probability mass function (pmf) is

f(x|p)={1p,x=0,p,x=1.

Mean and Variance

The mean is

mean=p.

The variance is

var=p(1p).

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).

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