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Let X₁, X₂, X3, X, denote a random sample of size n from the population distributed with the following probability density function: c) d) e) f) g) [(0+1)x, f(x: 0) = {0 0, if 0

Let X₁, X₂, X3, X, denote a random sample of size n from the population distributed with the following probability density function: c) d) e) f) g) [(0+1)x, f(x: 0) = {0 0, if 0

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 27E
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Let X₁, X₂, X3, X, denote a random sample of size n from the population distributed with the following probability density function: d) e) f) g) f(x; 0) = {(0+1)xº, if 0<x< 1 elsewhere Suppose that is a uniform minimum variance unbiased estimator of 8. Show that the variance of 6, Var(8) = (0+1)2 Use part d) of question 2 to show that is a consistent estimator of 8. Show that In(X) is a sufficient estimator of 8. [Hint: Use one-parameter regular exponential family). Estimate 8 using the method of moment estimator.
Transcribed Image Text:Let X₁, X₂, X3, X, denote a random sample of size n from the population distributed with the following probability density function: d) e) f) g) f(x; 0) = {(0+1)xº, if 0<x< 1 elsewhere Suppose that is a uniform minimum variance unbiased estimator of 8. Show that the variance of 6, Var(8) = (0+1)2 Use part d) of question 2 to show that is a consistent estimator of 8. Show that In(X) is a sufficient estimator of 8. [Hint: Use one-parameter regular exponential family). Estimate 8 using the method of moment estimator.
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