Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. 0 x < 0 +² F(x)= 0≤x≤ 4 16 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 3). 0.5625 (b) Calculate P(2.5 ≤ x ≤ 3). 0.1719 (c) Calculate P(x > 3.5). 0.2344 (d) What is the median checkout duration ? [solve 0.5 = F(ū)]. (e) Obtain the density function f(x). f(x) = F'(x) (f) Calculate E(X). (g) Calculate V(X) and a V(x) (h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(x)]. 0≤x < 4 otherwise

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