"GivenanytworandomvariablesXandY ,bythelinearityofexpectationswehaveE[X Y ]= E[X] E[Y ].Prove that, when X and Yare independent, Var[X Y ] = Var[X] + Var[Y ]. Which of the following arguments proves the claim?

(a)Var(aX + bY ) = a2Var(X) + b2Var(Y ) for any two r.v.'s X, Y=Var(X + (1)Y ) = Var(X) + Var(Y ).

(b)Var(X Y ) = E(X2) E(Y 2) = E(X2) + E(Y 2) = Var(X) + Var(Y ) = Var(X) + Var(Y )

(c)Var(X Y ) = Var(X + Y ) 2Var(Y ) = Var(X) + Var(Y ) = Var(X) + Var(Y ).

(d)By Corollary 3.4 Var(X + (Y )) = Var(X) + Var(Y ) = Var(X) + Var(Y ).

(e)none of these"