Bernoulli distribution - Maple Help

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Statistics[Distributions][Bernoulli] - Bernoulli distribution

 Calling Sequence Bernoulli(p) BernoulliDistribution(p)

Parameters

 p - probability of success

Description

 • The Bernoulli distribution is a discrete probability distribution with probability function given by:

$f\left(t\right)=\mathrm{piecewise}\left(t=0,1-p,t=1,p,0\right)$

 subject to the following conditions:

$0\le p,p\le 1$

 • The Bernoulli distribution comes about as a consequence of a single Bernoulli trial .  Success of the Bernoulli trial is indicated with x=1 and failure is indicated with x=0, where a success occurs with probability p.  The parameter p is also referred to as the Bernoulli probability parameter.
 • Note that the Bernoulli command is inert and should be used in combination with the RandomVariable command.

Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$
 > $X:=\mathrm{RandomVariable}\left(\mathrm{Bernoulli}\left(p\right)\right):$
 > $\mathrm{ProbabilityFunction}\left(X,0\right)$
 ${1}{-}{p}$ (1)
 > $\mathrm{ProbabilityFunction}\left(X,1\right)$
 ${p}$ (2)
 > $\mathrm{Mean}\left(X\right)$
 ${p}$ (3)
 > $\mathrm{Variance}\left(X\right)$
 ${p}{}\left({1}{-}{p}\right)$ (4)