Chapter 5.5, Problem 14E

Let T have at distribution with r degrees of freed dom. Show that $E\left(T\right)=0$ provided that $r\ge 2$, and $\mathrm{var}\left(T\right)=\frac{r}{\left(r-2\right)}$ provided that $r\ge 3$, by first finding $E\left(Z\right),E\left(1/\sqrt{U}\right),E\left(Z^2\right).$ and $E\left(1/U\right)$.