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. 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. 2.

$E[X]=p$

3. 3.

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

4. 4.

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

Title Bernoulli random variable BernoulliRandomVariable 2013-03-22 11:54:01 2013-03-22 11:54:01 Riemann (23) Riemann (23) 7 Riemann (23) Definition msc 60-00 Bernoulli distribution BernoulliDistribution2 GeometricDistribution2