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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 (III) The approximate variance of the maximum likelihood estimator of a is α √n (IV) None of the above. Hint: The approximate variance of the maximum likelihood estimator of a parameter is , where I (0) is the Fisher information which is defined by nI(0) I(0) O (II) (IV) O (III) O (1) -E ² log f(X;0) 2020

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 (III) The approximate variance of the maximum likelihood estimator of a is α √n (IV) None of the above. Hint: The approximate variance of the maximum likelihood estimator of a parameter is , where I (0) is the Fisher information which is defined by nI(0) I(0) O (II) (IV) O (III) O (1) -E ² log f(X;0) 2020

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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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 (III) The approximate variance of the maximum likelihood estimator of a is α √n (IV) None of the above. Hint: The approximate variance of the maximum likelihood estimator of a parameter is , where I (0) is the Fisher information which is defined by nI(0) I(0) O (II) (IV) O (III) O (1) -E ² log f(X;0) 2020
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 (III) The approximate variance of the maximum likelihood estimator of a is α √n (IV) None of the above. Hint: The approximate variance of the maximum likelihood estimator of a parameter is , where I (0) is the Fisher information which is defined by nI(0) I(0) O (II) (IV) O (III) O (1) -E ² log f(X;0) 2020
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