Is there a well-known prob. distribution (or a combination thereof) that has pdf: $\frac{1}{\sqrt{\pi}}t^{-1/2} e^{-t}$ on $t \ge 0$ and $0$ everywhere else.
Find distribution that has pdf $\frac{1}{\sqrt{\pi}}t^{-1/2} e^{-t}$ on the positive reals.
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probability
2 Answers
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The pdf you listed is known as $\chi^2$-distribution with $1$ degree of freedom, i.e. it is the pdf $f_X(t)$ of $X=\frac12Z^2$, where $Z$ is the standard normal random variable.
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0@Haderlump The $\chi^2$ random variable is defined as $Z^2$, your density is that of $\frac{1}{2} Z^2$. See the edit. – 2012-08-27
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It's the $\Gamma(\frac{1}{2},1)$ distribution.