Suppose (X1, X2) has a joint pdf fX1,X2 (x1, x2) = e(x1+x2) , for x1 > 0, x2 > 0

(a) Find the marginal distribution of X1

(b) Find the conditional distribution of X2 given X1 = x1

(c) Use either (a) or (b) to show that X1 and X2 are independent

(d) Find the joint density of Y1 = X1 + X2 and Y2 = X1/(X1 + X2).