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i) Find the conditional distribution of the likelihood function given the function of the statistic, Ô = ₁X₁. Hint: Apply ƒ(L(0)|g(Ô,0)). ii) Based on i) above, is ô: = Σ₁ X₁ a sufficient statistic? Justify your answer. iii) Show whether or not >, is a consistent estimator of the parameter 1/2.

i) Find the conditional distribution of the likelihood function given the function of the statistic, Ô = ₁X₁. Hint: Apply ƒ(L(0)|g(Ô,0)). ii) Based on i) above, is ô: = Σ₁ X₁ a sufficient statistic? Justify your answer. iii) Show whether or not >, is a consistent estimator of the parameter 1/2.

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 31CR
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a) Let X₁, X₂,..., Xn be a random sample of size n from population X. Suppose that X has the following probability mass function: f (x; 0) = {0 (1 - 0)x-1, lo, i) Find the conditional distribution of the likelihood function given the function of the statistic, Ô = 1 X₁. Hint: Apply f(L(0)|g(8,0)). n ii) Based on i) above, is Ô = Σ₁ X¿ a sufficient statistic? Justify your answer. iii) Show whether or not >, is a consistent estimator of the parameter 1. x = 1,2,3,... elsewhere
Transcribed Image Text:a) Let X₁, X₂,..., Xn be a random sample of size n from population X. Suppose that X has the following probability mass function: f (x; 0) = {0 (1 - 0)x-1, lo, i) Find the conditional distribution of the likelihood function given the function of the statistic, Ô = 1 X₁. Hint: Apply f(L(0)|g(8,0)). n ii) Based on i) above, is Ô = Σ₁ X¿ a sufficient statistic? Justify your answer. iii) Show whether or not >, is a consistent estimator of the parameter 1. x = 1,2,3,... elsewhere
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