Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 3 down vote favorite

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.

share|improve this question

2 Answers

up vote 6 down vote accepted

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.

share|improve this answer
@did Thanks for fixing the typo. – Sasha Aug 27 '12 at 19:45
You are welcome. – Did Aug 27 '12 at 20:12
I get $\frac{t^{-1/2}e^{-t/2}}{\sqrt{2}\sqrt{\pi}}$. – Haderlump Aug 27 '12 at 20:37
@Haderlump The $\chi^2$ random variable is defined as $Z^2$, your density is that of $\frac{1}{2} Z^2$. See the edit. – Sasha Aug 27 '12 at 20:39
up vote 2 down vote

It's the $\Gamma(\frac{1}{2},1)$ distribution.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.