8.19 Suppose that Y₁, Y2, . . ., Y, denote a random sample of size n from a population with an exponential distribution whose density is given by (1/0)e-y/0, f(y) = 0, y > 0, elsewhere. If Y(1) = min(Y₁, Y2, ..., Yn) denotes the smallest-order statistic, show that Ô = nY (1) is an unbiased estimator for and find MSE(Ô). [Hint: Recall the results of Exercise 6.81.]
8.19 Suppose that Y₁, Y2, . . ., Y, denote a random sample of size n from a population with an exponential distribution whose density is given by (1/0)e-y/0, f(y) = 0, y > 0, elsewhere. If Y(1) = min(Y₁, Y2, ..., Yn) denotes the smallest-order statistic, show that Ô = nY (1) is an unbiased estimator for and find MSE(Ô). [Hint: Recall the results of Exercise 6.81.]
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
Question 8.19 from Mathematical statistics with applications (Wackerly):
![8.19
Suppose that Y₁, Y2, . . ., Y, denote a random sample of size n from a population with an
exponential distribution whose density is given by
(1/0)e-y/0,
f(y)
=
0,
y > 0,
elsewhere.
If Y(1)
=
min(Y₁, Y2, ..., Yn) denotes the smallest-order statistic, show that Ô = nY (1) is an
unbiased estimator for and find MSE(Ô). [Hint: Recall the results of Exercise 6.81.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb90e355c-abe9-45d7-b8d1-631ace6b1e69%2Ff4aea7c9-cbf7-4cab-b594-6fcc92849b61%2F47qlnmi_processed.png&w=3840&q=75)
Transcribed Image Text:8.19
Suppose that Y₁, Y2, . . ., Y, denote a random sample of size n from a population with an
exponential distribution whose density is given by
(1/0)e-y/0,
f(y)
=
0,
y > 0,
elsewhere.
If Y(1)
=
min(Y₁, Y2, ..., Yn) denotes the smallest-order statistic, show that Ô = nY (1) is an
unbiased estimator for and find MSE(Ô). [Hint: Recall the results of Exercise 6.81.]
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 2 steps with 2 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