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Let X₁, X2, ..., Xn be a random sample from a Beta distribution with the pdf f(x; a) = axa-¹ for 0

Let X₁, X2, ..., Xn be a random sample from a Beta distribution with the pdf f(x; a) = axa-¹ for 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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[STATISTICS] MULTIPLE CHOICE: Which option is correct?

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Let X₁, X2,...,xn be a random sample from a Beta distribution with the pdf f(x; a) = axa-¹ for 0<x< 1, and zero otherwise. Which statement is correct? (1) The approximate variance of the maximum likelihood estimator of a is (II) The approximate variance of the maximum likelihood estimator of a is 2. (III) The approximate variance of the maximum likelihood estimator of a is Vn (IV) None of the above. Hint: The approximate variance of the maximum likelihood estimator of a parameter is the Fisher information which is defined by nI(0) I(0) = −E O (IV) O (II) O (III) O (1) ² log f(X;0) მომე where I (0) is
Transcribed Image Text:Let X₁, X2,...,xn be a random sample from a Beta distribution with the pdf f(x; a) = axa-¹ for 0<x< 1, and zero otherwise. Which statement is correct? (1) The approximate variance of the maximum likelihood estimator of a is (II) The approximate variance of the maximum likelihood estimator of a is 2. (III) The approximate variance of the maximum likelihood estimator of a is Vn (IV) None of the above. Hint: The approximate variance of the maximum likelihood estimator of a parameter is the Fisher information which is defined by nI(0) I(0) = −E O (IV) O (II) O (III) O (1) ² log f(X;0) მომე where I (0) is
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