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 --# F(x) 16 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 3). x < 0 0≤x < 4 (b) Calculate P(2.5 ≤ x ≤ 3). (c) Calculate P(x > 3.5). (d) What is the median checkout duration ? [solve 0.5 = = F(μ)]. (f) Calculate E(X). (e) Obtain the density function f(x). f(x) = f'(x) -{ (g) Calculate V(X) and V(X) 0x 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 --# F(x) 16 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 3). x < 0 0≤x < 4 (b) Calculate P(2.5 ≤ x ≤ 3). (c) Calculate P(x > 3.5). (d) What is the median checkout duration ? [solve 0.5 = = F(μ)]. (f) Calculate E(X). (e) Obtain the density function f(x). f(x) = f'(x) -{ (g) Calculate V(X) and V(X) 0x 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)].
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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
--#
F(x)
16
x < 0
1 4 ≤ x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X ≤ 3).
(c) Calculate P(x > 3.5).
0≤x < 4
(b) Calculate P(2.5 ≤ x ≤ 3).
(f) Calculate E(X).
(d) What is the median checkout duration ? [solve 0.5 = = F(μ)].
(e) Obtain the density function f(x).
f(x) = f'(x)
-{
(g) Calculate V(X) and
V(X)
0x
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%2F19a5c20d-d5cb-480c-bcde-dc1d0d3b3ef4%2Fd1432f6e-750e-457c-a9f0-5c10e1dbee6a%2Fdjhb2ff_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
--#
F(x)
16
x < 0
1 4 ≤ x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X ≤ 3).
(c) Calculate P(x > 3.5).
0≤x < 4
(b) Calculate P(2.5 ≤ x ≤ 3).
(f) Calculate E(X).
(d) What is the median checkout duration ? [solve 0.5 = = F(μ)].
(e) Obtain the density function f(x).
f(x) = f'(x)
-{
(g) Calculate V(X) and
V(X)
0x
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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