Question

Let X denote the amount of time a book on two-hour reserve is actually checked out,...

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)].

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