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a) b) c) Show that for any &> 0 and S, ===₁ X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. 1110 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8. Let ₁ = X₁+²x₂+2x₁-X¹ and ₂ = (X₁ + X₂ + X3 + X₁) be two unbiased estimators of 8. Which one of the two estimators is more efficient?

a) b) c) Show that for any &> 0 and S, ===₁ X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. 1110 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8. Let ₁ = X₁+²x₂+2x₁-X¹ and ₂ = (X₁ + X₂ + X3 + X₁) be two unbiased estimators of 8. Which one of the two estimators is more efficient?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3,..., X has the following probability density function (exe-e a) b) c) f(x; 0) = x! 0, " for x = 0,1,2,... elsewhere Show that for any &> 0 and S₂ = 1X₁, lim P(|S₂ - 0 ≥ ) = 0. 12-00 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. Let 0₁ = X₁+²x₂+2x₁-X and Ô₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which 4 one of the two estimators is more efficient? d) What is the Cramer-Rao lower bound for the variance of the unbiased estimator of the parameter 9? e) Use the one-parameter regular exponential family definition to find the functions, h(x), c(0), w(0) and t(x).
Transcribed Image Text:Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3,..., X has the following probability density function (exe-e a) b) c) f(x; 0) = x! 0, " for x = 0,1,2,... elsewhere Show that for any &> 0 and S₂ = 1X₁, lim P(|S₂ - 0 ≥ ) = 0. 12-00 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. Let 0₁ = X₁+²x₂+2x₁-X and Ô₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which 4 one of the two estimators is more efficient? d) What is the Cramer-Rao lower bound for the variance of the unbiased estimator of the parameter 9? e) Use the one-parameter regular exponential family definition to find the functions, h(x), c(0), w(0) and t(x).
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