Consider the mixed effects model m=a+bizi+06 with bi=N(u'I7-2)' {1} The mean and variance of y; are, respectively, 0 (a, 31372 +02) 0 [a + cm, 2'37} + 02) O (0+2m, 02 +13) 0 (a + mi\"! 1-2) {2) The conditional density of b,- given 1;,- is normal with mean and variance p.- (a,p) = W and of = W. What is the expected value nib? O pf+o O {ah-+0? O HEM? O a? {3} The EM algorithm for estimating a and p, assuming a' and 1' are known, would take (an, pg) to (61,];1) by minimizing over (Gnu), the expectation of the following with respect to the densities of the 5,- given the 11,-, O 2:; (m a moi/oz +2110 ear/3 O 23.; (y.- aii.-:c.-)'I +2L1Ebs w)\" 0 EL (9.- ab.-z.-)\"/a* O 2'; (in wig/r\" {4) The EM update for an to an is given by 0 a1 = y 1171 2,11 mm.- (anal-50) 0 a1 = 2:1 wen- (Gown) 0 a1 = y + 1171 9:1 mm.- (Guano) O 0.1 = n'1 2L1 33"\" (ar) _ (5) The EM update for jo to /1 is given by O M =9 Om=niEr / (ao, HO) O M1 = Ho O /1 = 41