BernoulliDistribution

The Bernoulli distribution: $1$ with probability $p$, $0$ with probability $1-p$.

BernoulliDistribution(p)an inert distribution object — carries $p$, unevaluated.

Typed signatures

Type	Package	Applies
(real<0..1>) -> distribution	statistics	always

Domain: Statistics

Details

• $PDF$ is $1-p$ at $0$, $p$ at $1$, and $0$ elsewhere.
• $CDF$ is $0$ below $0$, $1-p$ on $[0,1)$, and $1$ from $1$ on.
• $Mean = p$, $Variance = p(1-p)$, both exact.
• RandomVariate draws a single uniform and compares it to $p$.

Examples

Basic #

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In$\operatorname{PDF}(\mathrm{BernoulliDistribution}(\frac{1}{3}), 1)$Out$\frac{1}{3}$

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In$\operatorname{CDF}(\mathrm{BernoulliDistribution}(\frac{1}{3}), 0)$Out$\frac{2}{3}$

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In$\mathrm{mean}(\mathrm{BernoulliDistribution}(\frac{1}{3}))$Out$\frac{1}{3}$

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In$\mathrm{Variance}(\mathrm{BernoulliDistribution}(\frac{1}{3}))$Out$\frac{2}{9}$

About

Examples	4

See also: GeometricDistribution, BinomialDistribution, PDF, CDF