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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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