Geometric Random Variable

A Random Variable $X$ is said to have a geometric distribution with parameter $p$ for $k=1,2,...$ if: $P(X=k)=p(1-p{)}^{k-1}$

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Notation:

A geometric random variable is denoted as $X\text{textasciitilde}Geo(p)$

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Properties:

A Random Variable $X$ with a geometric distribution with parameter $p$ for $k=1,2,...$ has:

Name	Property	Value
Expected Value	$\mathbb{E}(X)$	$\frac{1}{p}$
Variance	$Var(X)$	$\frac{1-p}{p^2}$