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): x² = 0 ≤ x < 4 16 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 2). (b) Calculate P(1.5 ≤ X ≤ 2). (c) Calculate P(X > 2.5). (d) What is the median checkout duration μ? [solve 0.5 = F(M)]. (e) Obtain the density function f(x). f(x) = F'(x) (f) Calculate E(X). (g) Calculate V(X) and σx. V(X) 0 ≤ x < 4 otherwise (h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(X)].
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): x² = 0 ≤ x < 4 16 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 2). (b) Calculate P(1.5 ≤ X ≤ 2). (c) Calculate P(X > 2.5). (d) What is the median checkout duration μ? [solve 0.5 = F(M)]. (e) Obtain the density function f(x). f(x) = F'(x) (f) Calculate E(X). (g) Calculate V(X) and σx. V(X) 0 ≤ x < 4 otherwise (h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(X)].
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.CT: Chapter Test
Problem 4CT
Related questions
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.
0
X < 0
F(X):
x²
=
0 ≤ x < 4
16
1
4 ≤ x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X ≤ 2).
(b) Calculate P(1.5 ≤ X ≤ 2).
(c) Calculate P(X > 2.5).
(d) What is the median checkout duration μ? [solve 0.5 = F(M)].
(e) Obtain the density function f(x).
f(x) = F'(x)
(f)
Calculate E(X).
(g) Calculate V(X) and σx.
V(X)
0 ≤ x < 4
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%2Fbedd5747-9476-45b7-ab2c-0211874b0421%2Fe08f1f7c-ddcd-45dc-b4de-f782505862d5%2Fmky7qi_processed.png&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.
0
X < 0
F(X):
x²
=
0 ≤ x < 4
16
1
4 ≤ x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X ≤ 2).
(b) Calculate P(1.5 ≤ X ≤ 2).
(c) Calculate P(X > 2.5).
(d) What is the median checkout duration μ? [solve 0.5 = F(M)].
(e) Obtain the density function f(x).
f(x) = F'(x)
(f)
Calculate E(X).
(g) Calculate V(X) and σx.
V(X)
0 ≤ x < 4
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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