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Let X₁, X₂, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: d) e) f) ((0+1)xº, if 0 < x < 1 elsewhere f(x; 0) = {(0₁- Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance (0+1)² of ê, Var() = n Use part d) of question 2 to show that Ô is a consistent estimator of 0. Show that ₁ ln(X) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family].

Let X₁, X₂, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: d) e) f) ((0+1)xº, if 0 < x < 1 elsewhere f(x; 0) = {(0₁- Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance (0+1)² of ê, Var() = n Use part d) of question 2 to show that Ô is a consistent estimator of 0. Show that ₁ ln(X) 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.CR: Chapter 13 Review
Problem 7CR
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Let X₁, X₂, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: d) e) f) ((0+1)xº, if 0 < x < 1 elsewhere f(x; 0) = {(0₁- Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance (0+1)² of ê, Var(8) = n Use part d) of question 2 to show that Ô is a consistent estimator of 0. Show that exponential family]. In (X₁) is a sufficient estimator of 0. [Hint: Use one-parameter regular
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: d) e) f) ((0+1)xº, if 0 < x < 1 elsewhere f(x; 0) = {(0₁- Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance (0+1)² of ê, Var(8) = n Use part d) of question 2 to show that Ô is a consistent estimator of 0. Show that exponential family]. In (X₁) is a sufficient estimator of 0. [Hint: Use one-parameter regular
Let X₁, X₂, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: d) e) f) ((0+1)xº, if 0 < x < 1 elsewhere f(x; 0) = {(0₁- Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance (0+1)² of ê, Var(8) = n Use part d) of question 2 to show that Ô is a consistent estimator of 0. Show that exponential family]. In (X₁) is a sufficient estimator of 0. [Hint: Use one-parameter regular
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: d) e) f) ((0+1)xº, if 0 < x < 1 elsewhere f(x; 0) = {(0₁- Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance (0+1)² of ê, Var(8) = n Use part d) of question 2 to show that Ô is a consistent estimator of 0. Show that exponential family]. In (X₁) is a sufficient estimator of 0. [Hint: Use one-parameter regular
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