here is another one without solution
let be observations of variable X and be observations of a variable . Let , , Var(X) = , Var(Y) =
a) prove that , where a, b are constants.
b) prove that Var(aX+b) = Var(X), where a, b are constants.
c) prove that Var +Var = Var(X) + Var(Y)
d) given the following observations on (X, Y), verify the equality in (c)
e)Let Z= aX +bY and W = cX +dY so that in matrix notation
Show that Var(Z) +Var(W) = Var(X) +Var(Y)