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 +² F(x)= 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 ≤ 3). 0.5625 (b) Calculate P(2.5 ≤ x ≤ 3). 0.1719 (c) Calculate P(x > 3.5). 0.2344 (d) What is the median checkout duration ? [solve 0.5 = F(ū)]. (e) Obtain the density function f(x). f(x) = F'(x) (f) Calculate E(X). (g) Calculate V(X) and a V(x) (h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(x)]. 0≤x < 4 otherwise

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

Q5

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
+²
F(x)=
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 ≤ 3).
0.5625
(b) Calculate P(2.5 ≤ x ≤ 3).
0.1719
(c) Calculate P(x > 3.5).
0.2344
(d) What is the median checkout duration ? [solve 0.5 = F(ū)].
(e) Obtain the density function f(x).
f(x) = F'(x)
(f) Calculate E(X).
(g) Calculate V(X) and a
V(x)
(h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(x)].
0≤x < 4
otherwise
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 +² F(x)= 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 ≤ 3). 0.5625 (b) Calculate P(2.5 ≤ x ≤ 3). 0.1719 (c) Calculate P(x > 3.5). 0.2344 (d) What is the median checkout duration ? [solve 0.5 = F(ū)]. (e) Obtain the density function f(x). f(x) = F'(x) (f) Calculate E(X). (g) Calculate V(X) and a V(x) (h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(x)]. 0≤x < 4 otherwise
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman