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Show that for any e > 0 and Sn = Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8. Let 0₁ = X₁+2X₂+2X-X₁ and ₂ = (X₁ + X2 + X3 + X₁) be two unbiased estimators of 6. Which one of the two estimators is more efficient? ) 1X₁, lim P(IS-01 ≥ 8) = 0. 71-00

Show that for any e > 0 and Sn = Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8. Let 0₁ = X₁+2X₂+2X-X₁ and ₂ = (X₁ + X2 + X3 + X₁) be two unbiased estimators of 6. Which one of the two estimators is more efficient? ) 1X₁, lim P(IS-01 ≥ 8) = 0. 71-00

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 (0%e-0 f(x; 0) = x! 0, I for x = 0,1,2,... elsewhere Show that for any &> 0 and Sn = 1X₁, lim P(|S₁ - 0 ≥ ) = 0. 71-00 Show that a statistic S,, in a) is the maximum likelihood estimator of the parameter 8. Let 0₁ = X₁+2X2+2X₁-X4 and ₂ = (X₁ + X2 + X3 + X4) be two unbiased estimators of 0. Which one of the two estimators is more efficient? ) What is the Cramer-Rao lower bound for the variance of the unbiased estimator of the parameter 0? 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 (0%e-0 f(x; 0) = x! 0, I for x = 0,1,2,... elsewhere Show that for any &> 0 and Sn = 1X₁, lim P(|S₁ - 0 ≥ ) = 0. 71-00 Show that a statistic S,, in a) is the maximum likelihood estimator of the parameter 8. Let 0₁ = X₁+2X2+2X₁-X4 and ₂ = (X₁ + X2 + X3 + X4) be two unbiased estimators of 0. Which one of the two estimators is more efficient? ) What is the Cramer-Rao lower bound for the variance of the unbiased estimator of the parameter 0? 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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