Bernoulli random variable

$X$ is a Bernoulli random variable with parameter $p$ if

$f_{X}(x)=p^{x}(1-p)^{1-x}$ , $x=\{0,1\}$

Parameters:

$\star$

$p\in[0,1]$

Syntax:

$X\sim Bernoulli(p)$

Notes:

1.

$X$ represents the number of successful results in a Bernoulli trial. A Bernoulli trial is an experiment in which only two outcomes are possible: success, with probability $p$ , and failure, with probability $1-p$ .
2.

$E[X]=p$
3.

$Var[X]=p(1-p)$
4.

$M_{X}(t)=pe^{t}+(1-p)$

Title	Bernoulli random variable
Canonical name	BernoulliRandomVariable
Date of creation	2013-03-22 11:54:01
Last modified on	2013-03-22 11:54:01
Owner	Riemann (23)
Last modified by	Riemann (23)
Numerical id	7
Author	Riemann (23)
Entry type	Definition
Classification	msc 60-00
Synonym	Bernoulli distribution
Related topic	BernoulliDistribution2
Related topic	GeometricDistribution2