27. As a different generalization, let (XA,.I" . . , XA,.p) be independent vectors, each having a p-variate normal distribution with common covariance matrix and with expectation E( XA,,; ) = p.(i) + a~l + fJ;i) , L a~i) = L fJ;i) = 0 x for all i , and consider the hypothesis that each of p.U), a~), fJ;i) (A = 1, ... , a; JI = 1, . .. ,

b) is independent of i. (i) Give explicit expressions for the matrices Y and Z and the parameters 1J = E(Y) being tested. (ii) Give an example of a situation in which this problem might arise.