2. Let X₁, X, be a random sample from the Pareto distribution with the p.d.f.: f(x0) = (0/x²) 1(x>0), 0<<∞.(20) a) Show that X(1) min (X) is a CSS(Complete Sufficient Statistic) for 0.(10) (hint: Y= X(₁)~p(Y 0 ) b) Find the MVUE of 0.(10) (hint: X, = 0U₂, U₁ ~ƒ(u) = (1/u² ) 1.0) (u), U(1) ~ g(u) = n/u"+¹,1
2. Let X₁, X, be a random sample from the Pareto distribution with the p.d.f.: f(x0) = (0/x²) 1(x>0), 0<<∞.(20) a) Show that X(1) min (X) is a CSS(Complete Sufficient Statistic) for 0.(10) (hint: Y= X(₁)~p(Y 0 ) b) Find the MVUE of 0.(10) (hint: X, = 0U₂, U₁ ~ƒ(u) = (1/u² ) 1.0) (u), U(1) ~ g(u) = n/u"+¹,1
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:2. Let X₁, X, be a random sample from the Pareto distribution with the p.d.f.:
f(x0)= (0/x²) 1(x>0), 0<0<∞.(20)
a) Show that X(1) min (X) is a CSS(Complete Sufficient Statistic) for 0.(10)
(hint: Y= X(₁)~p(Y<yl0)=G(yl)-1-(0/y)", y> 0 )
b) Find the MVUE of 0.(10) (hint: X, = 0U₂, U₁~f(u) = (1/²) (1) (u), U(1) g(u) = n/u+¹,1<u<∞ )
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