Bernoulli random variable
$X$ is a Bernoulli random variable with parameter $p$ if
${f}_{X}(x)={p}^{x}{(1p)}^{1x}$, $x=\{0,1\}$
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 $1p$.

2.
$E[X]=p$

3.
$Var[X]=p(1p)$

4.
${M}_{X}(t)=p{e}^{t}+(1p)$
Title  Bernoulli random variable 

Canonical name  BernoulliRandomVariable 
Date of creation  20130322 11:54:01 
Last modified on  20130322 11:54:01 
Owner  Riemann (23) 
Last modified by  Riemann (23) 
Numerical id  7 
Author  Riemann (23) 
Entry type  Definition 
Classification  msc 6000 
Synonym  Bernoulli distribution 
Related topic  BernoulliDistribution2 
Related topic  GeometricDistribution2 