Suppose that a sequence of mutually independent and identically distributed discrete randomvariables X₁, X₂, X3,..., X has the following probability density function(0%e-ex!0.a)b)c)f(x; 0) =for x = 0,1,2,...elsewhereShow that for any > > 0 and S₂ = 1X₁, lim P(|S₁-01 ≥ ) = 0.348Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. (Let Ô₁ = X₁+2X²+2X₁-X₁ and ₂ = (X₁ + X₂ + X3 + X4) 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 thparameter 8?e) Use the one-parameter regular exponential family definition to find the functions,h(x), c(0), w(0) and t(x).

We will use Chebychev's inequality to calculate the required limit of probability. To obtain the MLE…

Answered: n Show that for any &> 0 and S₁ = 1X₁,…

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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5. Let X1,.., Xn ~ Geo(8). (a) Find a 90% asymptotic confidence interval for 0. (b) Find a 99% asymptotic lower confidence intervals for o = 1/0, the expected number of trials until the first success.
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18. Show that for type lII population - x/0 dp O
A car repair company (that receives payments on a daily basis) is going to select which car repair offer toaccept (A, B, C or D) in order to maximize the company incomea) Calculate the expected value (mean) of the different repair offers and indicate which repair offer (A, B, Cor D) to accept (i.e. the one with the maximum expected value).b) If the repair is completed in less than or equal to 3 days, the company will receive an extra one timepayment of 1000 TL in all the offers. Considering this new situation, will the repair that offers the maximumincome change?
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