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{\bf Question}

Suppose that a random variable $X$ has the pdf

$$\ds\frac{1}{\sqrt{2\pi}}x^{-\frac{1}{2}}e^{-\frac{x}{2}},\ \
0<x<\infty.$$

Using a list of distributions, give the names and the parameters
of two distributions that this pdf matches.

\medskip

{\bf Answer}

It matches with the $\chi^2$ distribution for $p=1$.  Since
$\Gamma\left(\ds \frac{1}{2}\right)=\sqrt{\pi}$

It matches with the gamma distribution with $\alpha=\ds
\frac{1}{2}$ and $\beta=2$.

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