# t-student distribution [duplicate]

I've got this problem:

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?

• Because this is a homework/self-study question, you should add the self-study tag. See stats.stackexchange.com/tags/self-study/info – Patrick Coulombe Feb 25 '15 at 3:41
• 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 6:28