Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the CDF, cumulative density function, is the following: F(x) = 0 x < 0 x2 16 0 ≤ x ≤ 4 1 4 ≤ x Use the cumulative density function to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 2). (b) Calculate P(1.5 ≤ X ≤ 2). (c) Calculate P(X > 2.5). (d) What is the median checkout duration mu tilde? [solve 0.5 = F(mu tilde)]. (e) Obtain the probability density function, f(x). f(x) = F '(x) = (f) Calculate E(X). (g) Calculate V(X) and σx. V(X) = σx = (h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].