B) Let X1,X2, .,Xn be a random sample from a N(u, o2) population with both parametersunknown. Consider the two estimators S2 and ô? for o? where S2 is the sample variance, i.e.s2 =E,(X, – X)² and ở² = 'E".,(X1 – X)². [X = =E-, X, is the sample mean].%3Dn-1Li%3D1[Hint:a2(п-1)52-~x~-1 which has mean (n-1) and variance 2(n-1)]i)Show that S2 is unbiased for o2. Find variance of S2.ii)Find the bias of 62 and the variance of ô2.iii)Show that Mean Square Error (MSE) of ô2 is smaller than MSE of S?.iv)Show that both S2 and ô? are consistent estimators for o?.

Given that X1, X2,........,Xn follows Normal distribution with unknown parameters. Note : According…

Answered: Show that S2 is unbiased for o2. Find…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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HOUGHTON MIFFLIN HARCOURT

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