Problem 4 This problem outlines a proof of the following equalities. If X = aX + b and Y = cy +d, then ( a) PRY = PX, Y, (b) Cov[X, Y] = ac Cov[X, Y]. (a) Show that X - E[X] = a(X - E[X]), Y - E[Y] = c(Y - E[Y]). (b) Use part (a) to show that Cov X, Y = ac Cov [ X, Y] . (c) Show that Var[X] = a2 Var[X] and Var[Y] = c2 Var[Y]. (d) Combine parts (b) and (c) to relate px y and px,Y