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
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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 64E
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda5a8041-aeed-45a6-a7fc-c4165c2d9a1f%2F812a0e6b-87d4-450a-9c46-5581cef87444%2Fvg5ngbq_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
+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
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning