Let the independent random variables X1 and X2 be N(0,1) and 2(r), respectively. Let Y1 = X1/X2/r

Question:

Let the independent random variables X1 and X2 be N(0,1) and χ2(r), respectively. Let Y1 = X1/√X2/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. (This is another, equivalent, way of finding the pdf of T.)