exponential random variable

$X$ is a exponential random variable with parameter $\lambda >0$ if its probability density function is given for $x>0$ by

$f_X(x)=\lambda e^{-\lambda x}.$

To denote this, one usually writes $X\sim Exp(\lambda )$.

For an exponential random variable $X$:

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

2. The expected value of $X$ is given by $E[X]=\frac{1}{\lambda }$

3. The variance of $X$ is given by $Var[X]=\frac{1}{{\lambda }^2}$

4. The moments of $X$ are given by $M_X(t)=\frac{\lambda }{\lambda -t}$

5. It is interesting to note that $X$ is a gamma random variable with an $\alpha$ 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