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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 30E
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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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