GATE 2022 ST – Question 38

Multivariate Analysis · Multivariate Normal and Wishart Distributions · 2 marks · Multiple choice

Four independent observations (3,6)ᵀ,(4,4)ᵀ,(5,7)ᵀ,(4,7)ᵀ come from a bivariate normal population. If μ̂,Σ̂ are their MLEs,find Σ̂μ̂.

(3.5,10)ᵀ
(7.5,4)ᵀ
(4,13.5)ᵀ
(10,3.5)ᵀ

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Correct answer: (A) (3.5,10)ᵀ

Explanation

The sample mean is μ̂=(4,6)ᵀ. Centering the four points gives Σ̂=(1/4)[[2,1],[1,6]]=[[.5,.25],[.25,1.5]]. Multiplication gives (.5·4+.25·6,.25·4+1.5·6)=(3.5,10). **A**.

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