Let (X1 j1,..., X1 jn; X2 j1,..., X2 jn;...; Xaj1,..., Xajn), j =

1,...,

b, be a sample from an an-variate normal distribution. Let E(Xijk ) = ξi , and denote by 

ii the matrix of covariances of (Xi j1,..., Xijn) with (Xi j1,..., Xi jn).

Suppose that for all i, the diagonal elements of 

ii are = τ 2 and the off-diagonal elements are = ρ1τ 2, and that for i = i all n2 elements of 

ii are = ρ2τ 2.

(i) Find necessary and sufficient conditions on ρ1 and ρ2 for the overall abn × abn covariance matrix to be positive definite.
(ii) Show that this model agrees with that of