7.15 Assume that X₁, X2, X3, X4 are independent and normally distributed with E[X₁] = 100 E[X₂] = 90 E[X3] = 95 E[X4] = 105 Var[X₁] = 30 Var[X₂] = 20 Var[X3] = 25 Var[X4] = 15. (a) What is the distribution of S = X₁ +X-2 + X3 + X4? Can we use the central limit theorem in this case? (b) Find E[S], Var[S], and o [S]. (e) Compute P(S≤ 390). Is the answer different from P(S < 390)?
7.15 Assume that X₁, X2, X3, X4 are independent and normally distributed with E[X₁] = 100 E[X₂] = 90 E[X3] = 95 E[X4] = 105 Var[X₁] = 30 Var[X₂] = 20 Var[X3] = 25 Var[X4] = 15. (a) What is the distribution of S = X₁ +X-2 + X3 + X4? Can we use the central limit theorem in this case? (b) Find E[S], Var[S], and o [S]. (e) Compute P(S≤ 390). Is the answer different from P(S < 390)?
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
![7.15 Assume that X₁, X₂, X3, X4 are independent and normally distributed with
E[X₁] = 100 E[X₂] = 90
E[X3] = 95
E[X4] = 105
Var[X₂] = 20
Var[X3] = 25
Var[X4] = 15.
(a) What is the distribution of S = X₁ + X-2+ X3 + X4? Can we use the central
limit theorem in this case?
(b) Find E[S], Var[S], and o [S].
(e) Compute P(S≤ 390). Is the answer different from P(S < 390)?
Var[X₁] = 30
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F962f1d6a-8f28-40e1-8e00-3b445e7f8a1f%2F148e5ab5-4d95-4aab-8441-2628eeb98dfb%2Fccylzkk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7.15 Assume that X₁, X₂, X3, X4 are independent and normally distributed with
E[X₁] = 100 E[X₂] = 90
E[X3] = 95
E[X4] = 105
Var[X₂] = 20
Var[X3] = 25
Var[X4] = 15.
(a) What is the distribution of S = X₁ + X-2+ X3 + X4? Can we use the central
limit theorem in this case?
(b) Find E[S], Var[S], and o [S].
(e) Compute P(S≤ 390). Is the answer different from P(S < 390)?
Var[X₁] = 30
-
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 20 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman