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 ? 1). (b) Calculate P(0.5 ? X ? 1). (c) Calculate P(X > 1.5). (d) What is the median checkout duration mu tilde? [solve 0.5 = F(mu tilde)]. (e) Obtain the density function f(x). f(x) = F?'(x) = (f) Calculate E(X). (g) Calculate V(X) and ?x. V(X) = ?x = (h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].