geometric random variable

A geometric random variablePlanetmathPlanetmath with parameter p(0,1] is one whose density distribution functionMathworldPlanetmath is given by


This is denoted by XGeo(p).


  1. 1.

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

  2. 2.

    The expected valueMathworldPlanetmath of a geometric random variable is given by E[X]=1-pp, and the varianceMathworldPlanetmath by Var[X]=1-pp2

  3. 3.

    The moment generating function of a geometric random variable is given by MX(t)=p1-(1-p)et.

Title geometric random variable
Canonical name GeometricRandomVariable
Date of creation 2013-03-22 11:54:06
Last modified on 2013-03-22 11:54:06
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 14
Author mathcam (2727)
Entry type Definition
Classification msc 62-00
Classification msc 60-00
Classification msc 92-01
Classification msc 92B05
Synonym geometric distribution