geometric random variable
A geometric random variable^{} with parameter $p\in (0,1]$ is one whose density distribution function^{} is given by
$${f}_{X}(x)=p{(1p)}^{x},x=0,1,2,\mathrm{\dots}$$ 
This is denoted by $X\sim Geo(p)$.
Notes:

1.
A standard application of geometric random variables is where $X$ represents the number of failed Bernoulli trials before the first success.

2.
The expected value^{} of a geometric random variable is given by $E[X]=\frac{1p}{p}$, and the variance^{} by $Var[X]=\frac{1p}{{p}^{2}}$

3.
The moment generating function of a geometric random variable is given by ${M}_{X}(t)=\frac{p}{1(1p){e}^{t}}$.
Title  geometric random variable 

Canonical name  GeometricRandomVariable 
Date of creation  20130322 11:54:06 
Last modified on  20130322 11:54:06 
Owner  mathcam (2727) 
Last modified by  mathcam (2727) 
Numerical id  14 
Author  mathcam (2727) 
Entry type  Definition 
Classification  msc 6200 
Classification  msc 6000 
Classification  msc 9201 
Classification  msc 92B05 
Synonym  geometric distribution 