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:

• $p\in [0,1]$

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. $M_X(t)=p{e}^t+(1-p)$