here is another one without solution

Q2

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)

if