Geometric Distribution

Definition

$Y\sim \mathrm{Geom}(p)=NB(1,p)$ where $p$ is a probability in each experiment

The number of failures before the 1st success

Properties

PDF

$f(y)=p(1-p{)}^y,y\in {\mathbb{N}}_0$

Mean

$E(X)=\frac{1-p}{p}$

Variance

$\mathrm{Var}(X)=\frac{1-p}{p^2}$