3n Ô = - 1 Зп — 1 ÔMLE = ( - min{Y1, ..., Y,} %3D 3n 3n is an unbiased estimator of 0. Determine the density function of 0. Note that this describes the sampling distribution of 6.

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
1. (8 points) Suppose that Y1,..., Yn is a random sample from a population whose
density is
f (y\0) = 30°y¬4,
y > 0,
for some parameter 0 > 0. As we showed in class, the maximum likelihood estimator of 0 is
ÔMLE
min{Y1,..., Yn} and whose density function is
.—Зп—1
fôMLE (7) = 3n0³nx
provided x > 0. As shown on Midterm #1,
Зп — 1
Зп — 1
OMLE
E ) min{Y1, · · . ,
3n
3n
is an unbiased estimator of 0. Determine the density function of 0. Note that this describes
the sampling distribution of Ô.
Transcribed Image Text:1. (8 points) Suppose that Y1,..., Yn is a random sample from a population whose density is f (y\0) = 30°y¬4, y > 0, for some parameter 0 > 0. As we showed in class, the maximum likelihood estimator of 0 is ÔMLE min{Y1,..., Yn} and whose density function is .—Зп—1 fôMLE (7) = 3n0³nx provided x > 0. As shown on Midterm #1, Зп — 1 Зп — 1 OMLE E ) min{Y1, · · . , 3n 3n is an unbiased estimator of 0. Determine the density function of 0. Note that this describes the sampling distribution of Ô.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 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