21. Let X₁, X2, ..., Xn be a random sample from a population X with density function [0x0-1 for 0 < x < 1 f(x; 0) = 0 otherwise, 1 where > 1 is parameter. Show that - ln(X₂) is a uniform minimum variance unbiased estimator of 1.
21. Let X₁, X2, ..., Xn be a random sample from a population X with density function [0x0-1 for 0 < x < 1 f(x; 0) = 0 otherwise, 1 where > 1 is parameter. Show that - ln(X₂) is a uniform minimum variance unbiased estimator of 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
Related questions
Question
![21. Let X₁, X2, ..., Xn be a random sample from a population X with density
function
0x0-1
for 0 < x < 1
f(x; 0) =
0
otherwise,
where > 1 is parameter. Show that - ln(X₂) is a uniform minimum
variance unbiased estimator of ¼.
n
i=1
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44fc1f94-d26a-4e82-91d6-4e2568333d67%2F4d32f001-49b3-455d-aee2-0a54a315aaa7%2F7hy9q3t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:21. Let X₁, X2, ..., Xn be a random sample from a population X with density
function
0x0-1
for 0 < x < 1
f(x; 0) =
0
otherwise,
where > 1 is parameter. Show that - ln(X₂) is a uniform minimum
variance unbiased estimator of ¼.
n
i=1
=
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