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![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
x²
25
1
X<0
0<x<5
(c) Calculate P(X > 4.5).
5≤X
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X ≤ 4),
(b) Calculate P(3.5 ≤ x ≤ 4).
(d) What is the median checkout duration ? [solve 0.5 = F(p)].](https://content.bartleby.com/qna-images/question/16cbd5c2-fb88-434e-ad72-693f4b78f768/ea1b63ff-8c2b-4be8-bd4f-372facb12c36/lmw7l7l_processed.jpeg)
![(e) Obtain the density function f(x).
f(x)
F'(x)
=
(f) Calculate E(X).
(g) Calculate V(X) and
V(X)
0≤x<5
otherwise
(h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(X)].](https://content.bartleby.com/qna-images/question/16cbd5c2-fb88-434e-ad72-693f4b78f768/ea1b63ff-8c2b-4be8-bd4f-372facb12c36/btjjha_processed.jpeg)
