Please provide clear explanation and show your steps. Thank you!

3. CDF to PMF (10 points) Suppose that X is a discrete random variable that takes integer values from 1 to 100 (both inclusive), and has cumulative distribution function (CDF) Fx (x) = Pr(X > 100 (Thus, for example, F(1) = 1 . 2/10100 and F(2) = 2 . 3/10100 and so on.) Find the probability mass function (pmf ) for X. In other words, provide a formula for px (a) that is correct for any integer x in {1, 2, . .., 100}