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Let X₁, X2,..., Xn be a random sample from a Beta distribution with the pdf f(x; α) = 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.

Let X₁, X2,..., Xn be a random sample from a Beta distribution with the pdf f(x; α) = 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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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. nI(0) Hint: The approximate variance of the maximum likelihood estimator of a parameter is the Fisher information which is defined by 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. nI(0) Hint: The approximate variance of the maximum likelihood estimator of a parameter is the Fisher information which is defined by 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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