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.) (d) What is the median checkout duration ? [solve 0.5 = F()]. (e) Obtain the density function f(x). f(x) = F '(x) = (f) Calculate E(X).

kissesbxtch69oE3

kissesbxtch69oE3

Answered question

2022-12-05

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.)
(d) What is the median checkout duration ? [solve 0.5 = F()].
(e) Obtain the density function f(x). f(x) = F '(x) =
(f) Calculate E(X).

Answer & Explanation

Bryson Carlson

Bryson Carlson

Beginner2022-12-06Added 10 answers

d) The median checkout for the duration that is 50% of the probability:
So, P( x < a ) = 0.5
(x^2 / 25) = 0.5
x^2 = 12.5
x = 3.5355
e) The probability density function can be evaluated by taking the derivative of the cdf as follows:
pdf f(x) = d(F(x)) / dx = x / 12.5
f) The expected value of X can be evaluated by the following formula from limits - to + :
E(X) = integral ( x . f(x)).dx limits: - to +
E(X) = integral ( x^2 / 12.5)
E(X) = x^3 / 37.5 limits: 0 to 5
E(X) = 5^3 / 37.5 = 3.3333

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