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

f(x) = ((x^2)/4) , 0 <= x <= 2

1 , 2<= x


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

(a) P(X %u2264 1)

(b) P(0.5 %u2264 X %u2264 1)

(c) P(X > 1.5)

(d) The median checkout duration [solve 0.5 = F(mew)]

(e) Use F'(x) to obtain the density function f(x)
(f) Calculate E(X)

(g) Calculate V(X) and %u03C3x
(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge

E[h(X)].