Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. F(x) = 0 x < 0 x2 16 0 ≤ x < 4 1 4 ≤ x Use the cdf 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 ? [solve 0.5 = F()]. (e) Obtain the 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)].