" Consider that a random variable Y has the following density function, (« y*-1 fy) = Osyso elsewhere where a is known, and satisfies a > 0, and 0 is an unknown parameter. Let Y, be an independent random variable from the distribution fly), with i=1,.,n a) Calculate the bias for the estimator ô = Ỹ = 2 Y/. b) Calculate the mean square error of the estimator ê = Ỹ = 2 /n. cl Propose an unbiased estimator of A and show that it is upbiased

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 that a random variable Y has the following density function,
(«y*-1
fG) =} 0a
0sys0
elsewhere
where a is known, and satisfies a > 0, and 0 is an unknown parameter. Let Y, be an independent random variable from
the distribution f(y), with i=1,..,n
a) Calculate the bias for the estimator ê = Ỹ = 2 Y/n.
b) Calculate the mean square error of the estimator ô = Y = 2
c) Propose an unbiased estimator of 0 and show that it is unbiased.
Transcribed Image Text:: Consider that a random variable Y has the following density function, («y*-1 fG) =} 0a 0sys0 elsewhere where a is known, and satisfies a > 0, and 0 is an unknown parameter. Let Y, be an independent random variable from the distribution f(y), with i=1,..,n a) Calculate the bias for the estimator ê = Ỹ = 2 Y/n. b) Calculate the mean square error of the estimator ô = Y = 2 c) Propose an unbiased estimator of 0 and show that it is unbiased.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
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