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Show that ₁ ln(X₁) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family].

Show that ₁ ln(X₁) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family].

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
Section13.1: Continuous Probability Models
Problem 21E
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4.STATISTICAL INFERENCE
Question 2 f

Let X₁, X2, X3, ..., Xn denote a random sample of size n from the population distributed with the following probability density function: f) ((0+1)xº, if 0 < x < 1 elsewhere f(x; 8) = {(0- 0) Show that 1 ln(X₁) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family].
Transcribed Image Text:Let X₁, X2, X3, ..., Xn denote a random sample of size n from the population distributed with the following probability density function: f) ((0+1)xº, if 0 < x < 1 elsewhere f(x; 8) = {(0- 0) Show that 1 ln(X₁) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family].
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