Suppose that a sequence of mutually independent and identically distributed discrete randomvariables X₁, X₂, X3, ..., Xn has the following probability density functiona)b)c)f(x; 0) =0xe-0x!0,Jfor x = 0,1,2,...elsewhereShow that for any & > 0 and S₂ = = =₁ X₁, lim P(|S₂ − 0| ≥ ɛ) = 0.nn-00one of the two estimators is more efficient?Show that a statistic S₁ in a) is the maximum likelihood estimator of the parameter 8.Let Ô₁ =X1+2X2+2X3-X44¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 0. Which

We will use Chebychev's inequality to find the required limit. To find the MLE of the parameter,…

) -) ) Show that for any &> 0 and Sn = 1X₁, lim P(|S₂ - 0 ≥ ) = 0. 12-00 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. X₁+2X2+2X3-X4 Let Ô₁ = and 6₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 0. Wh one of the two estimators is more efficient?

) -) ) Show that for any &> 0 and Sn = 1X₁, lim P(|S₂ - 0 ≥ ) = 0. 12-00 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. X₁+2X2+2X3-X4 Let Ô₁ = and 6₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 0. Wh one of the two estimators is more efficient?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.1: Continuous Probability Models

Problem 31E: Show that each function defined as follows is a probability density function on the given interval;...

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