12. Under the assumptions of the preceding problem suppose that E(X;) = t = Ej_lo;A, E(Y,) = 1/;= Ej-1b;A with the n X s matrices A = (a ;j) and B = (b; j) of rank s. Then the experiment based on the Y, is more informative than that based on the X; if and only if B'B - A'A is nonnegative definite. [There exists a nonsingular matrix F such that F'A'AF = I and F'B'BF = A, where I is the identity and A is diagonal . The transformation X' = FX, Y' = FY reduces the situation to that of Problem 11.] Note. The results of Problems 11 and 12 no longer hold when 0 2 is unknown. See Hansen and Torgersen (1974).