Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is Use the cdf to obtain the following:

a.

b.

c.

d. The median checkout duration [solve

e. to obtain the density function f(x)

f. E(X)

g. V(X) and h. If the borrower is charged an amount when checkout duration is X, compute the expected charge E[h(X)].

h(X) 5 X2 sX Fr(x)

.5 5 F(m

| m )] | P(X . 1.5)

P(.5 # X # 1)

P(X # 1)

F(x) 5 d 0 x , 0 x2 4

0 # x , 2 1 2 # x