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a) b) 2/ Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, X has the following probability density function (0xe-0 x! c) 100% QUESTION 2 f(x; 0) = } for x = 0,1,2,... elsewhere Show that for any e > 0 and Sn = 1X₁, lim P(|Sn - 01 ≥ ) = 0. n 318 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8. Let 0₁ = X₁+2X²+2X-X4 and 0₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Wr one of the two estimators is more efficient?

a) b) 2/ Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, X has the following probability density function (0xe-0 x! c) 100% QUESTION 2 f(x; 0) = } for x = 0,1,2,... elsewhere Show that for any e > 0 and Sn = 1X₁, lim P(|Sn - 01 ≥ ) = 0. n 318 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8. Let 0₁ = X₁+2X²+2X-X4 and 0₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Wr one of the two estimators is more efficient?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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a) b) 2 / 6 Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, X has the following probability density function 0xe-0 x! 0, c) 100% QUESTION 2 f(x; 0) = for x = 0,1,2,... elsewhere F Show that for any e > 0 and S₁ = -1 X¡, lim P(|S, − 0| ≥ ɛ) = 0. 1-00 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. X₁ +2X₂+2X3=X4 Let 6₁ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 9. Wh one of the two estimators is more efficient?
Transcribed Image Text:a) b) 2 / 6 Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, X has the following probability density function 0xe-0 x! 0, c) 100% QUESTION 2 f(x; 0) = for x = 0,1,2,... elsewhere F Show that for any e > 0 and S₁ = -1 X¡, lim P(|S, − 0| ≥ ɛ) = 0. 1-00 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. X₁ +2X₂+2X3=X4 Let 6₁ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 9. Wh one of the two estimators is more efficient?
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