(c) Under Hoμ₁ = μ₂, let us write µ₁ = µ₂ = µ. Prove that the maximum likelihood estimator of u, assuming Ho is true, is the pooled estimator == Σ "1X: +2=1Y; mX+nY m+n m+n (d) Using part (a), (b) and (c), prove that the likelihood ratio can be written as max=2= L(µ, µ) maxμ₁₂ (μ1, 2) = exp 1 mn 2 (m+n) (x - (e) Using part (d), prove that the critical region of the likelihood ratio test with significance level a is of the form C = {√ mn m+n -

(c) Under Hoμ₁ = μ₂, let us write µ₁ = µ₂ = µ. Prove that the maximum likelihood estimator of u, assuming Ho is true, is the pooled estimator == Σ "1X: +2=1Y; mX+nY m+n m+n (d) Using part (a), (b) and (c), prove that the likelihood ratio can be written as max=2= L(µ, µ) maxμ₁₂ (μ1, 2) = exp 1 mn 2 (m+n) (x - (e) Using part (d), prove that the critical region of the likelihood ratio test with significance level a is of the form C = {√ mn m+n -

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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