Let X, Y, Z have joint pdf f(x, y, z) = 2(x + y + z)/3, 0 (a) Find the marginal probability density functions of X, Y, and Z. (c) Are X, Y , and Z independent? (d) Calculate E(X2Y Z + 3XY 4Z2). (e)...

Let X, Y, Z have joint pdf f(x, y, z) = 2(x + y + z)/3, 0 <><><> (a) Find the marginal probability density functions of X, Y, and Z.

(c) Are X, Y , and Z independent? (d) Calculate E(X2Y Z + 3XY 4Z2). (e) Determine the cdf of X, Y, and Z. (f) Find the conditional distribution of X and Y , given Z = z, and evaluate E(X + Y |z). (g) Determine the conditional distribution of X, given Y = y and Z = z, and compute E(X|y, z).