\begin{definition}[Definition:Chi Distribution]
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X = \hointr 0 \infty$. 
Let $r$ be a strictly positive integer.
$X$ is said to have a '''chi distribution''' with $r$ degrees of freedom {{iff}} it has probability density function:
:$\map {f_X} x = \dfrac 1 {2^{\paren {r / 2} - 1} \map \Gamma {r / 2} } x^{r - 1} e^{- x^2 / 2}$
where $\Gamma$ denotes the gamma function.
This is written: 
:$X \sim \chi_r$
\end{definition}