Category:Chi-Squared Distribution

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This category contains results about the chi-squared 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-squared distribution with $r$ degrees of freedom if and only if it has probability density function:

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

where $\Gamma$ denotes the gamma function.

This is written:

$X \sim \chi^2_r$