Exercise 2 (Cumulative distribution function) Assume the random variable U is uniformly distributed within [0,1] and consider the transformation X = g1(U), where 91 is the inverse of a swim 9(3): if [I and :3" ';> D. (a) Check that g is a valid cdf. (13) Bonus task: Show that g is in fact the cdf of X. {Bonus points) ((3) Bonus task: Derive the pdf of X . (Bonus points)