6. A likelihood argument provides additional support for pooling the two indepen dent sample covariance matrices to estimate a common covariance matrix in the case of two normal populations. Give the likelihood function L(/1, M2, E), for two independent sample sizes n1 and n2 from Np(M1, E) and Np(M2, E) pop- ulations, respectively. Show that this likelihood is maximized by the choices (1 = 1, M2 = 12 and H n1 + 12 - 2 E = [(n1 - 1)S1+ (n2 - 1)S2] = S n1 + n2 n1 + 12 pooled