3. Let X be a random variable that maps the sample space (1 onto 29?. Let s be a cur-algebra of subsets of $3\". Show that the collection of sets 9'0 that consists of all preimages of sets A from sf! is a a-algebra. That is, show that 9}, = {F : F = X '1(A), A E at} is a a-algebra. 4. Let X be a random variable mapping the probability space (0, 9', P) into a measurable space (%, 5s), and let PX(A) = P [X '1(A)] for A e m. Show that ($8, st, PX) is a probability space; that is, show that PX satises the axioms of probability