Let X and Y be two normal random variables with respective mean of X an Y , respective variance of 2 X an 2 Y respectively, and covariance of XY . Set Z = aX bY + c with a, b and c being constants. Compute:

(a) E[Z], E[Z|X], E[Z|Y], E[Z|X, Y]

(b) V[Z], V[Z|X], V[Z|Y], V[Z|X, Y]

(c) E[E[Z|X]], E[E[Z|Y]], E[E[Z|X, Y]]

(d) V[E[Z|X]], V[E[Z|Y]], V[E[Z|X, Y]]

(e) E[V[Z|X]], E[V[Z|Y]], E[V[Z|X, Y]]