GATE 2022 ST – Question 39
X∼N₃(μ,Σ),μ=(2,−3,2)ᵀ,Σ has rows (4,−1,1),(−1,2,a),(1,a,2). The partial correlation of X₂ and X₃ given X₁ is 5/7. Find a.
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Correct answer: (A) 1
Explanation
Conditional covariance is a−(−1)(1)/4=a+1/4. Both conditional variances are 2−1/4=7/4. Thus partial correlation=(a+1/4)/(7/4)=(4a+1)/7. Equating to 5/7 gives **a=1, A**.