I. JUMPS IN THE CDF Fix a probability triplet (S, F, P). Let X be a random variable. Fix a E R. Recall that P[X = a] is equal to the height of the jump in the CDF Fx (x) at the point a. That is, P[X = a] = Fx (a) - Fx(a ). This problem proves it. a) Use the definition of An \\A to prove that { X e (a -,, a]} } {X = a}. b) By continuity of probability together with part (a), we conclude that limn - P[X E (a - 2, a] = P[X = a]. Use this to conclude the result about the jump in the CDF at point a. c) Use the fact P[X = a] = Fx (a) - Fx (a ) to prove that if the CDF is continuous at all points x E R then P[X = x] = 0 for all x E R