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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let X1, X₂,..., X₁ be a random sample from a Beta distribution with the pdf ƒ(x; a) = axª-¹ for 0< x < 1, and zero otherwise. Which statement is correct? (1) â = X is the maximum likelihood estimator of a and is a consistent estimator of a. (II) â = X is the maximum likelihood estimator of a and is NOT a consistent estimator of a. is the maximum likelihood estimator of a and is a consistent estimator of a. (III) â = (IV) â = O (IV) O (1) O (III) O (II) -n Zi-1 log(X₂) -n Σ1 log(X₂) i=1 is the maximum likelihood estimator of a and is NOT a consistent estimator of a.
Transcribed Image Text:Let X1, X₂,..., X₁ be a random sample from a Beta distribution with the pdf ƒ(x; a) = axª-¹ for 0< x < 1, and zero otherwise. Which statement is correct? (1) â = X is the maximum likelihood estimator of a and is a consistent estimator of a. (II) â = X is the maximum likelihood estimator of a and is NOT a consistent estimator of a. is the maximum likelihood estimator of a and is a consistent estimator of a. (III) â = (IV) â = O (IV) O (1) O (III) O (II) -n Zi-1 log(X₂) -n Σ1 log(X₂) i=1 is the maximum likelihood estimator of a and is NOT a consistent estimator of a.
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