Compute the conditional PDF fxy(xly) of X given Y = y for the examples in Assignment 5: (a) The joint PDF of (X, Y) is f(x, y) = 9(x2 + 7) for r e (0, 1), y e (0,2), and f(x, y) = 0 otherwise. (b) The joint PDF of (X, Y) is f(x,y) = re -" for r > 0, y > 0, and f(r, y) =0 otherwise. (c) The joint PDF (X, Y) is f(x, y) = 2 for r E (0, y), y c (0, 1), and f(z, y) = 0 otherwise.Suppose that the joint PDF of (X, Y) is f(x,y) = c(1 + 7) for r e (0, 1), y e (0,2), and f(x, y) = 0 otherwise, where c is a constant. (a) What is the constant c? (b) Find P{X > Y}. We have 1 = / f(z,y) andy - [ [ c (23 + 4 ) dady - c (P y + zy]) so c =6/7. Moreover, -7y' + 3y +4 dy = 15 14 56 Let (X, Y) have joint PDF f(r, y) = re -y for x > 0, y > 0 and f(r, y) =0 otherwise. (a) Compute the marginal PDFs of X and Y. (b) Determine whether X and Y are independent. We have fx ( x ) = xe- " dy = re-?, fy(y ) = xe-*-ydr=e-", for I > 0 and y > 0 respectively. Hence f(r,y) = fx(x) - fy(y), so X and Y are independent. Let (X, Y) have joint PDF f(I, y) = c for r E (0, y), ye (0, 1) and f(x, y) =0 otherwise, where c is a constant. (a) What is the constant c? (b) Compute the marginal PDF's of X and Y. (c) Determine whether X and Y are independent. Since we obtain c = 2. Moreover, fx ( ) - [ 2 dy - 2 - 2x , s ( ) = [ '2 dx - 20 for r E (0, 1) and y c (0, 1) respectively. Hence f(r,y) / fx(x) - fv(y), so X and Y are not independent