64. Let (X\ j\" " ,X\jn; X2j\" " ,X2jn ; . .. ; X"j\, ,, ,,X"jn),j=l, .. . ,b,bea sample from an-variate normal distribution. Let E(X;jk) = i' and denote by ~;; the matrix of covariances of (X;j\ ' " '' X;jn) with (X;'j\' " '' X;'jn)' Suppose that for all i, the diagonal elements of ii are = -r 2 and the off-diagonal elements = PI-r 2, and that for; oF if all n2 elements of ii' are = P2-r 2 . (i) Find necessary and sufficient conditions on p\ and P2 for the overall abn X abn covariance matrix to be positive definite. (ii) Show that this model agrees with that of Problem 62 for suitable values of p\ and P2