A die is rolled 3 times. Let Z;, i = 1, 2,3 be the outcomes. (Assume they are independent of each other).Define random variables X, Y by: X = Z1+ %2+ 23, Y = ZI+Z2 -Z3 (i) Calculate Var(Z1 ) by using the formula Var(Z1) = E[Z?] - (E[ZI])? (ii) Show that Cov(X, Y) = Var(Z,) Hint: Use the properties of Covariance (pp 52-53 in textbook), and that Z; are i.i.d