Let X denote the amount of time a book on two-hour reserve is actually checked o

Question

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 x < 0 x2 16 0 x 4 1 4 x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)

(a) Calculate P(X 1)

(b) Calculate P(0.5 X 1)

(c) Calculate P(X > 1.5)

(d) What is the median checkout duration mu tilde? [solve 0.5 = F(mu tilde)].

(e) Obtain the density function f(x). f(x) = F'(x) =

(f) Calculate E(X)

(g) Calculate V(X) and x. V(X) = x =

(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

Explanation / Answer

a)

Note that

P(x<1) = F(1) = 1^2/16 = 0.0625 [ANSWER]

*******************

b)

Note that

P(0.5<x<1) = F(1) - F(0.5) = 1^2/16 - 0.5^2/16 = 0.046875 [ANSWER]

******************

c)

Note that

P(x>1.5) = 1 - F(1.5) = 1 - 1.5^2/16 = 0.859375 [ANSWER]

********************

d)

For the median m,

F(m) = 0.5

Hence,

m^2/16 = 0.5

m^2 = 8

m = sqrt(8) = 2.828427125 [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.