Example 17-8. X1, X2, and X3 is a random sample of size 3 from a population with meanvalue u and variance ơ². T,, T2, T3 are the estimators used to estimate mean value µ, where11T1= X1 + X2 – X3, T2= 2X1+3X3– 4X2 ,T3 =} (^X,+ X2 + X3)/3.and|(i) Are T1 and T2 unbiased estimators ?(ii) Find the value of A such that T3 is unbiased estimator for u.(iii) With this value of A is T3 a consistent estimator ?(iv) Which is the best estimator ?

Answered: Image /qna-images/answer/51156d30-8a91-4a53-be99-f7ffe27e515e.jpg

Answered: Example 17-8. X1, X2, and X3 is a…

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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Two different plasma etchers in a semiconductor factory have the same mean etch rate μ. However, machine 1 is newer than machine 2 and consequently has smaller variability in etch rate. We know that the variance of etch rate for machine 1 is σ12, and for machine 2, it is σ2 = σ 2 12 a . Suppose that we have n1 independent observations on etch rate from machine 1 and n2independent observations on etch rate from machine 2.(a) Show that ˆμ = +− α α X X ( ) 1 2 1 is an unbiased estimator of μ for any value of α between zero and one.(b) Find the standard error of the point estimate of μ in part (a).(c) What value of α would minimize the standard error of the point estimate of μ?(d) Suppose that a = 4 and n n 1 2 = 2 . What value of α would you select to minimize the standard error of the point estimate of μ? How “bad” would it be to arbitrarily choose α= . 0 5 in this case?
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