Consider a random sample X1,..., Xn with n > 3 from the exponential distribution with parameter > 0 and density f(x; A) = -e-=/A, r >0. Consider the following two estimators of A: 3 Â = ;£Xi, Ã= nX(1)- 3 i=1

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
Consider a random sample X1,..., X, with n > 3 from the exponential distribution
with parameter ) > 0 and density
1
f(x; A) =
x > 0.
Consider the following two estimators of X:
3
1
ΣΧ,
à = nX(1).
3
i=1
Transcribed Image Text:Consider a random sample X1,..., X, with n > 3 from the exponential distribution with parameter ) > 0 and density 1 f(x; A) = x > 0. Consider the following two estimators of X: 3 1 ΣΧ, Ã = nX(1). 3 i=1
(2) Calculate L = E(Ä|X1) and find its variance. Is the variance of L smaller than
the variance of Ä? Is L an estimator of X? Explain why this is.
(3) Construct an estimator which improves on à (you do not need to have a closed
form for it, but you do need to prove that it is an estimator).
Transcribed Image Text:(2) Calculate L = E(Ä|X1) and find its variance. Is the variance of L smaller than the variance of Ä? Is L an estimator of X? Explain why this is. (3) Construct an estimator which improves on à (you do not need to have a closed form for it, but you do need to prove that it is an estimator).
Expert Solution
steps

Step by step

Solved in 6 steps

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