exponential random variable

X is a exponential random variable with parameter λ>0 if its probability density functionMathworldPlanetmath is given for x>0 by


To denote this, one usually writes XExp(λ).

For an exponential random variable X:

  1. 1.

    X is commonly used to model lifetimes and duration between Poisson events.

  2. 2.

    The expected valueMathworldPlanetmath of X is given by E[X]=1λ

  3. 3.

    The varianceMathworldPlanetmath of X is given by Var[X]=1λ2

  4. 4.

    The moments of X are given by MX(t)=λλ-t

  5. 5.

    It is interesting to note that X is a gamma random variable with an α parameter of 1.

Title exponential random variable
Canonical name ExponentialRandomVariable
Date of creation 2013-03-22 11:54:23
Last modified on 2013-03-22 11:54:23
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 9
Author mathcam (2727)
Entry type Definition
Classification msc 62E15
Classification msc 06F20
Classification msc 11B65
Classification msc 05C15
Synonym exponential distribution