62. Let X be a gamma random variable with a = 3/2 and 3 = 1 and given X, Y has the following conditional density function: C(x) if xyx f(y|x) = { 0 - elsewhere Find the density function of T = max(X, Y). 1 Solution: Since C(x)dy = 2TC(r) we get C(x) = Since f(x, y) = f(x)f(y|x) 2 we get if x 0,xyx f(x, y) = 0 elsewhere R(T) [0, ) and F(t) = P(X t,Y 1 there is no need for integration, since T = X. Thus, by FTC + 2t f(t) = 2 re if 0 if 0 t1 t> 1 elsewhere