Let (0, F, P) be a probability space and X : 0 - R be a random variable. Denote the Borel o-algebra on R as B(R), and define the function Mx (B) = P(X-'(B)) for all B E B(R). Show that (R, B(R), Mx) is a probability space. Hint: Use the fact that P is a probability measure and the definition of a random variable. [2]