where sgn(.) denotes the signum function or sign function. 6. Let X, Y be two random variables and Z = aX + bY where a, b are constants. Show that (a) E[Z] = a E[X] + bE[Y], (b) Var(Z) = a2 Var(X) + 62 Var(Y) + 2ab Cov(X, Y). with parameters (1, 1 and #2, 0