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.

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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
=
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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