X−Y is N_p(0,2Σ). Standardize by (2Σ)^(−1/2) to obtain p independent standard normals. Their squared norm is (1/2)(X−Y)ᵀΣ⁻¹(X−Y), with **p degrees of freedom, A**.
More Multivariate Normal and Wishart Distributions questions
GATE 2026 ST Q58– X~N p(μ,Σ),Σ positive definite, and real A satisfies AᵀA=I. Let Y=AX. Which hold?
GATE 2026 ST Q59– For X=(X₁,…,X p)ᵀ~N p(0,Σ),Σ positive definite, which hold?
GATE 2025 ST Q23– A bivariate normal (X,Y) has means 3,4, variances 25,100 and covariance 50ρ,−1<ρ<1. If E(Y…
GATE 2025 ST Q30– X is 10-dimensional N₁₀(0,I). Let Y=ln√(XᵀX) and M Y(t)=E(e(tY)),t>−10. Find M Y(2)…
GATE 2025 ST Q45– Five iid bivariate N₂(0,I₂) vectors form rows of a 5×2 matrix X. Let W=XᵀX and…
GATE 2025 ST Q53– X~N₃(0,diag(4,9,4)),α=(2,0,−1)ᵀ,β=(1,1,1)ᵀ. Which hold?