3 Recall that two random variables X and Y are independent if pr(X S a, Y S b) = WM 5 a) -pr(Y S b) holds for all a, b E R. This should be covered in your prerequisites, but you can also refer to the Wikipedia page at: https://en.wikipedia.org/wiki/Independence_(probability_theory) Assume that X and Y are independent random variables. Prove that for any in vertible monotonic functions f and g, f (X ) and 9(Y) are independent. [Note The condition can be weakened to measurable functions, but in the later case the proof may require certain knowledge from measure theory. ]