Let (X1j1,...,X1jn; X2j1,...,X2jn; ... ; 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 (Xij1,...,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