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 25 0 ≤ x < 5 1 5 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)(g) Calculate V(X) and σx. V(X) = σx = (h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

quakbIi

quakbIi

Answered question

2022-11-26

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 25 0 ≤ x < 5 1 5 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(g) Calculate V(X) and σx. V(X) = σx =
(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

Answer & Explanation

Jadyn Huynh

Jadyn Huynh

Beginner2022-11-27Added 7 answers

g) The variance of X can be evaluated by the following formula from limits - to +
Var(X) = integral ( x^2 . f(x)).dx - (E(X))^2 limits: - to +
Var(X) = integral ( x^3 / 12.5).dx - (E(X))^2
Var(X) = x^4 / 50 | - (3.3333)^2 limits: 0 to 5
Var(X) = 5^4 / 50 - (3.3333)^2 = 13.8891
s.d(X) = sqrt (Var(X)) = sqrt (13.8891) = 3.7268
h) Find the expected charge E[h(X)] , where h(X) is given by:
h(x) = (f(x))^2 = x^2 / 156.25
The expected value of h(X) can be evaluated by the following formula from limits - to +
E(h(X))) = integral ( x . h(x) ).dx limits: - to +
E(h(X))) = integral ( x^3 / 156.25)
E(h(X))) = x^4 / 156.25 limits: 0 to 25
E(h(X))) = 25^4 / 156.25 = 2500

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