Can provide answers with some explanation.

Consider the mixed effects model 3;; = a+ biwz- +O'e.,;, with bi = N(,u.,1'2) . (1) The mean and variance of y,- are, respectively, 0 (a, 32372 +02) 0 (a + my, $372 + (72) O (a+ mm, 0'2 +13) 0 (41+ 132'\(3) The EM algorithm for estimating a and Mu, assuming o and T are known, would take (ao, Mo ) to (a1, M1 ) by minimizing over (a, M), the expectation of the following with respect to the densities of the b; given the yi, O En (yi - a - bizi)2 102 + Ex-, ( bi - 1 ) 2/ 72 O ER (yi - a - biz; )? + ER (bi - Re)? O En (yi - a - biz;)2/02 O En- (bi - 1 ) 2/ 7 2 (4) The EM update for an to a1 is given by Oal = y -n' El-1 xilli (ao, Mo) O al = EL Tilli (ao, Mo) O al = ytl Er, illi (ao, No) O al = n-1 Er xiMi (ao, Mo) - y (5) The EM update for Mo to /1 is given by OM = y OM = n-Er-1 Mi (ao, Mo) O M 1 = MO O M1 = al