Problem 1 50.0 points possible (graded, results hidden) Consider the mixed effects model yi = at biti toe;, with bi = N (u, T?). (3) The EM algorithm for estimating a and A, assuming o and T are known, would take (ao, Mo) to (a1, /1 ) by minimizing over (a, ), the expectation of the following with respect to the densities of the b; given the yi, O EN (yi - a - biz;)2102 + ER, (bi - 1)2/ 72 O EL- ( yi - a - biz.)? + ET- ( bi - 1)? O EL, (yi - a - biz.)- 102 O EN- (bi - 1 ) 2/ 72 (4) The EM update for an to a, is given by Oa = y-n- Er xiMi (ao, MO) O al = EM Timi (ao, Ho) On = gon ' Er, Tiki (ao, MO) O a = n-1 Er, TiMi (ao, HO) - y (5) The EM update for /o to / is given by O m =y OM =n' El Mi (ao, HO) OH1 = HO O /1 = al