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sities. Let X₁, X2,..., Xn be a random sample of size n from the density ƒx(x; 0) = 0(1 + x)−(¹+0) I(0,∞) (x), 0 > 0 Show that the density belongs to the one-parameter exponential class of den- Find a complete sufficient statistic, if there is one. Be able to provide justifica- tion/s why such statistic is complete and sufficient. Find the Cramer-Rao lower bound of the variance for unbiased estimators of 1/0.

sities. Let X₁, X2,..., Xn be a random sample of size n from the density ƒx(x; 0) = 0(1 + x)−(¹+0) I(0,∞) (x), 0 > 0 Show that the density belongs to the one-parameter exponential class of den- Find a complete sufficient statistic, if there is one. Be able to provide justifica- tion/s why such statistic is complete and sufficient. Find the Cramer-Rao lower bound of the variance for unbiased estimators of 1/0.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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sities. Let X₁, X2,..., Xn be a random sample of size n from the density fx(x; 0) = 0(1+x)−(¹ )−(1+0) I(0,∞)(x), 0 >0 Show that the density belongs to the one-parameter exponential class of den- Find a complete sufficient statistic, if there is one. Be able to provide justifica- tion/s why such statistic is complete and sufficient. Find the Cramer-Rao lower bound of the variance for unbiased estimators of 1/0.
Transcribed Image Text:sities. Let X₁, X2,..., Xn be a random sample of size n from the density fx(x; 0) = 0(1+x)−(¹ )−(1+0) I(0,∞)(x), 0 >0 Show that the density belongs to the one-parameter exponential class of den- Find a complete sufficient statistic, if there is one. Be able to provide justifica- tion/s why such statistic is complete and sufficient. Find the Cramer-Rao lower bound of the variance for unbiased estimators of 1/0.
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