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).
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).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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) =
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)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8edd889e-338a-4275-872c-5b2b400b4e22%2Fe39dd41d-f675-4a16-8cfe-ae6e3b153d34%2F18gn58h_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) =
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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