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Consider a random sample X1,..., Xn from the population distribution with density f(x; 8) = 0x°-1, r € (0, 1), and parameter 0 e (0, 00). (1) Verify that the Assumptions (1) and (2) of the Cramér-Rao Theorem (Theorem 2.22) are met.

Consider a random sample X1,..., Xn from the population distribution with density f(x; 8) = 0x°-1, r € (0, 1), and parameter 0 e (0, 00). (1) Verify that the Assumptions (1) and (2) of the Cramér-Rao Theorem (Theorem 2.22) are met.

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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Consider a random sample X1,..., Xn from the population distribution with density f(x; 8) = 0x°-1, r € (0, 1), and parameter 0 e (0, 00). (1) Verify that the Assumptions (1) and (2) of the Cramér-Rao Theorem (Theorem 2.22) are met.
Transcribed Image Text:Consider a random sample X1,..., Xn from the population distribution with density f(x; 8) = 0x°-1, r € (0, 1), and parameter 0 e (0, 00). (1) Verify that the Assumptions (1) and (2) of the Cramér-Rao Theorem (Theorem 2.22) are met.
Theorem 2.22 ( Cramér - Rao Inequality) Y. is a random sauple Suppore that from Po, o e X, - Let T(X,.., Xn) be au un bi ased eskmator of 8 (6), e. Eo T Let X~ Pe. Assume that the coudi'titious (D, (2), (3) below hold: P. has a pdf I pmf (1) For all O E and f (x; @) of exists for all o E e O and all x E N. such that P(XE No) for all & G@. 2) VoE O Đ logf (x,@) and 3 logt (x , ))) I(® € (0,00) for all e E + Here, I(6) is called F'SHER INFORMATION
Transcribed Image Text:Theorem 2.22 ( Cramér - Rao Inequality) Y. is a random sauple Suppore that from Po, o e X, - Let T(X,.., Xn) be au un bi ased eskmator of 8 (6), e. Eo T Let X~ Pe. Assume that the coudi'titious (D, (2), (3) below hold: P. has a pdf I pmf (1) For all O E and f (x; @) of exists for all o E e O and all x E N. such that P(XE No) for all & G@. 2) VoE O Đ logf (x,@) and 3 logt (x , ))) I(® € (0,00) for all e E + Here, I(6) is called F'SHER INFORMATION
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