5. ·O-/4.5 points 04 Submissions Used Let X denote the amount of time a book on

Question

5. ·O-/4.5 points 04 Submissions Used Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. 4 12SX Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate (X1). (b) Calculate P(O.5 sXS1) (c) Calculate P(X 1.5) (d) what is the median checkout duration ?? [solve 0.5- (e) Obtain the density function f(x) (f) Calculate E(X) (g) Calculate V(X) and Ox. (h) If the borrower is charged an amount h(X)-Xt when checkout duration is X, compute the expected charge Elh(X)] Need Help?Read It Talk to a Tutor

Explanation / Answer

a)
P(X<=1)
= F(1)
= 1^2/4 = 0.25

b)
P(0.5 < X< 1)
= F(1) - F(0.5)
= 0.25 - 0.25^2/4
= 0.234375

c)
P(X > 1.5) = 1 - P(X < 1.5)
= 1 - F(1.5)
= 1 - 1.5^2/4
= 0.4375

d)
P(X <a ) = 0.5
a^2/4 = 0.5
a^2 = 2
a= sqrt(2) = 1.414
e)
f(x) = d/dx F(x) = 1/4 * 2x = x/2

Please post rest questions again as we have to solve first 4 subparts by chegg policy

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