## Probability Density Function

The parameter is \(\nu\) and it is a positive integer.

It is the gamma distribution with \(\alpha=\frac{1}{2},\beta=2\)

\begin{equation*}
f(x;\nu)=\frac{x^{\left(\frac{\nu}{2}\right)-1}e^{-\frac{x}{2}}}{2^{\frac{\nu}{2}}\Gamma\left(\frac{\nu}{2}\right)}
\end{equation*}

For \(x\ge0\)

\(\nu\) is called the **number of degrees of freedom** (df) of
\(X\).

## Relation to the Normal Distribution

It is the distribution of a sum of the squares of \(\nu\) independent standard normal random variables.

## Usage

It is rarely used to model natural phenomena. However, it is used heavily in inferential statistics.