58. For the mixed model Xi} = J.L +

a, + + U;j (i=l, ... ,a; j=l, . . . ,n), where the B's and u's are as in Problem 57 and the a's are constants adding to zero, determine (with respect to a suitable group leaving the problem invariant) (i) a UMP invariant test of H: al = = au; (ii) a UMP invariant test of H: ~l = = ~a = 0 (~i = J.L + ai ); (iii) a test of H: aVa2 S 6 which is both UMP invariant and UMP unbiased.