Definition:Chi-Squared Distribution

Definition
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-squared distribution with $r$ degrees of freedom it has probability density function:


 * $\map {f_X} x = \dfrac 1 {2^{r / 2} \map \Gamma {r / 2} } x^{\paren {r / 2} - 1} e^{-x / 2}$

where $\Gamma$ denotes the gamma function.

This is written:


 * $X \sim {\chi_r}^2$

where $\chi$ is the Greek letter $\chi$ (chi).