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Consider a multivariate random sample X1, . . . , Xnwhich comes from p-dimensional multivariate distribution...

Consider a multivariate random sample X1, . . . , Xnwhich comes from p-dimensional multivariate distribution N(µ, Σ), with mean vector µ ∈ R p and the variance-covariance positive definite matrix Σ. Find the distribution and its parameters for the matrix nXTHX where H is the idempotent centering matrix H = In −1/n (1n ⊗ 1n ) and 1n is the n-dimensional vector of all 1’s.

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