Let X denote the amount of time a book on twohour reserve is

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) =

Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)

f(x) = F\'(x) =

(f)    E(X)


(g)    V(X) and _x

(h) If the borrower is charged an amount

h(X) = X² when checkout duration is X, compute the expected charge

E[h(X)].

Solution

A)

P(x<=2) = F(2)

= 2^2/25

= 0.16 [ANSWER]

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b)

P(1.5<=x<=2) = F(2) - F(1.5)

= 2^2/25 - 1.5^2/25

= 0.07 [ANSWER]

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c)

P(x>2.5) = 1 - F(2.5)

= 1 - 2.5^2/25

= 0.75 [ANSWER]

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D)

If F(u) = 0.5, then

u^2 / 25 = 0.5

u^2 = 12.5

u = 3.535533906 [ANSWER]

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