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I've got this problem: enter image description here

Here, if $Z,W$ are independent random variables, and $Z$ has normal standart distribution and $W$ has $\chi^2$ with $n$ degrees of freedom, $T=\frac{Z}{\sqrt{\frac{W}{n}}}$. I don't expect to find any problems in $b$ and $c$ parts, but in $a$, I don't know how to find the conditional density. How could I?

Xi'an
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LeviathanTheEsper
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  • Because this is a homework/self-study question, you should add the `self-study` tag. See http://stats.stackexchange.com/tags/self-study/info – Patrick Coulombe Feb 25 '15 at 03:41
  • If you can figure out b, then you should have no problem with the conditional density, by re-arranging terms in b. – StatsStudent Feb 25 '15 at 06:28

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