# Category:Cauchy Distribution

This category contains results about the Cauchy distribution.

Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \R$.

$X$ is said to have a Cauchy distribution if it has probability density function:

$\map {f_X} x = \dfrac 1 {\pi \gamma \paren {1 + \paren {\frac {x - x_0} \gamma}^2} }$

for some $\gamma > 0$.

This is written:

$X \sim \Cauchy {x_0} \gamma$

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