Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, ..., Xn has the following probability density function 0xe-0 x! 0, a) b) c) f(x; 0) = for x = 0,1,2,... elsewhere Show that for any & > 0 and S₂ = ₁ X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. 1 n Zi=1 - n n-8 Show that a statistic Sn in a) is the maximum likelihood estimator of the parameter 8. Let Ô₁ X₁+2X₂+2X3-X4 = 4 ¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which one of the two estimators is more efficient?
Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, ..., Xn has the following probability density function 0xe-0 x! 0, a) b) c) f(x; 0) = for x = 0,1,2,... elsewhere Show that for any & > 0 and S₂ = ₁ X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. 1 n Zi=1 - n n-8 Show that a statistic Sn in a) is the maximum likelihood estimator of the parameter 8. Let Ô₁ X₁+2X₂+2X3-X4 = 4 ¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which one of the two estimators is more efficient?
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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