Suppose that a sequence of mutually independent and identically distributed discrete randomvariables X₁, X₂, X3,..., X, has the following probability density functiona)b)c)d)e)f(x; 0) =Show that for any e > 0 and SnE=72exe-0x!0,Jfor x = 0,1,2,...elsewhere1 Xi, lim P(IS-01 ≥ 8) = 0.11-00Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8.Let ₁ = X1+2X2+2X3-X4¹ and ₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Whichone of the two estimators is more efficient?What is the Cramer-Rao lower bound for the variance of the unbiased estimator of theparameter 8?Use the one-parameter regular exponential family definition to find the functions,h(x), c(0), w (0) and t(x). Suppose that a sequence of mutually independent and identically distributed discrete randomvariables X₁, X₂, X3,..., X, has the following probability density functiona)b)c)d)e)f(x; 0) =Show that for any e > 0 and Sn=720xe-0x!0,Jfor x = 0,1,2,...elsewhere1 Xi, lim P(IS-01 ≥ 8) = 0.11-00Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8.Let ₁ = X1+2X2+2X3-X4¹ and ₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Whichone of the two estimators is more efficient?What is the Cramer-Rao lower bound for the variance of the unbiased estimator of theparameter 8?Use the one-parameter regular exponential family definition to find the functions,h(x), c(0), w (0) and t(x).

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

Answered: Show that for any & > 0 and Sn = Ei=1…

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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Show that for any & > 0 and Sn = Ei=1 Xi, lim P(|Sn-01 ≥ E) = 0. 11-00 a) b) Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8. Let 0₁ = X₁+2X2+2X₁-X and ₂ = (X₁ + X₂ + X₂ + X₁) be two unbiased estimators of 8. Which