Suppose that a sequence of mutually independent and identically distributed discrete randomvariables X₁, X₂, X3, X has the following probability density functionf(x: 0) =a)b)c)6e-0x!for x = 0,1,2,...0,elsewhereShow that for any e > 0 and S, X₁, lim P(|S, -01 ≥ £) = 0.Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8.Let 8₁ = X₁ +2x+2x₁-X and 6₂ = (X₁ + X₂ + X₁ + X₁) be two unbiased estimators of 8. Whichone of the two estimators is more efficient?d) What is the Cramer-Rao lower bound for the variance of the unbiased estimator of theparameter @?e) Use the one-parameter regular exponential family definition to find the functions,

As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Answered: a) b) c) Show that for any >0 and S,…

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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a) X is a normally distributed variable with mean u = 30 and standard deviation o = 4. Find i) P(x 21) iii) P(30
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a) b) c) Show that for any >0 and S, X₁. lim P(|S, -612 ) = 0. Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8. Let 8₁=X₁2X+2X-X₁ and 6₂ = (X₁ + X₂ + X₁ + X₂) be two unbiased estimators of 6. W one of the two estimators is more efficient?