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 x² 25 1 x < 0 0≤x<5 (c) Calculate P(X> 4.5). 5 ≤x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 4). (b) Calculate P(3.5 ≤ x ≤ 4).
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 x² 25 1 x < 0 0≤x<5 (c) Calculate P(X> 4.5). 5 ≤x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 4). (b) Calculate P(3.5 ≤ x ≤ 4).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 27E
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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
x²
25
1
X<0
0<x<5
(c) Calculate P(X > 4.5).
5≤X
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X ≤ 4),
(b) Calculate P(3.5 ≤ x ≤ 4).
(d) What is the median checkout duration ? [solve 0.5 = F(p)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16cbd5c2-fb88-434e-ad72-693f4b78f768%2Fea1b63ff-8c2b-4be8-bd4f-372facb12c36%2Flmw7l7l_processed.jpeg&w=3840&q=75)
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.
F(x)=
=
0
x²
25
1
X<0
0<x<5
(c) Calculate P(X > 4.5).
5≤X
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X ≤ 4),
(b) Calculate P(3.5 ≤ x ≤ 4).
(d) What is the median checkout duration ? [solve 0.5 = F(p)].
![(e) Obtain the density function f(x).
f(x)
F'(x)
=
(f) Calculate E(X).
(g) Calculate V(X) and
V(X)
0≤x<5
otherwise
(h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(X)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16cbd5c2-fb88-434e-ad72-693f4b78f768%2Fea1b63ff-8c2b-4be8-bd4f-372facb12c36%2Fbtjjha_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(e) Obtain the density function f(x).
f(x)
F'(x)
=
(f) Calculate E(X).
(g) Calculate V(X) and
V(X)
0≤x<5
otherwise
(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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