# Cauchy random variable

$X$ is a Cauchy random variable with parameters $\theta\in\mathbb{R}$ and $\beta>0\in\mathbb{R}$, commonly denoted $X\sim Cauchy(\theta,\beta)$ if

 $\displaystyle f_{X}(x)=\frac{1}{\pi\beta[1+(\frac{x-\theta}{\beta})^{2}]}.$

Cauchy random variables are used primarily for theoretical purposes, the key point being that the values $E[X]$ and $Var[X]$ are undefined for Cauchy random variables.

Title Cauchy random variable CauchyRandomVariable 2013-03-22 11:54:32 2013-03-22 11:54:32 mathcam (2727) mathcam (2727) 11 mathcam (2727) Definition msc 60A10 Cauchy distribution