Question: Given multivariate data X 1 ,..., X N (in R P ) in mean- deviation form, let P be a p x p matrix, and

Given multivariate data X₁,..., X_N(in R^P) in mean- deviation form, let P be a p x p matrix, and define Y_k= P^T X_kfor k = 1,..., N.

a. Show that Y₁,..., Y_N are in mean-deviation form. Let w be the vector in R^N with a 1 in each entry. Then [X₁.......... X_N]w = 0 (the zero vector in R^P.

b. Show that if the covariance matrix of X₁,..., X_N is S, then the covariance matrix of Y₁,..., Y_Nis P^TSP.

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