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) = 0 < x < 5 25 1 5 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 3). (b) Calculate P(2.5 ≤X ≤ 3). (c) Calculate P(X> 3.5).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 80E
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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) =
0 < x < 5
25
1
5 ≤ x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X ≤ 3).
(b) Calculate P(2.5 ≤X ≤ 3).
(c) Calculate P(X > 3.5).
(d) What is the median checkout duration ? [solve 0.5 = F(M)].
(e) Obtain the density function f(x).
f(x) = F'(x)
0 ≤x < 5
{
=
otherwise
(f) Calculate E(X).
(g) Calculate V(X) and ox
V(X)
ox
(h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(X)].
Transcribed Image Text: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) = 0 < x < 5 25 1 5 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 3). (b) Calculate P(2.5 ≤X ≤ 3). (c) Calculate P(X > 3.5). (d) What is the median checkout duration ? [solve 0.5 = F(M)]. (e) Obtain the density function f(x). f(x) = F'(x) 0 ≤x < 5 { = otherwise (f) Calculate E(X). (g) Calculate V(X) and ox V(X) ox (h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(X)].
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