Let the independent random variables X1 and X2 be N(0,1) and $\displaystyle X^{2}(r)$, respectively. Ley $\displaystyle Y1=\frac{X1}{\sqrt\frac{X^{2}}{r}}$ and Y2=X2.

a) Find the joint pdf of Y1 and Y2

b) Determine the marginal pdf of Y1 and show that Y1 has a t distribution

Thanks!