(30%) (EM algorithm) The monthly salary of n = 8000 employees are drawn from a company. Assume that there are three salary levels, including low income, middle income and high income. We denote the monthly salary of employee 2' by Y}, and the salary level of employee 2' by Zi. {Yi : 1 S i g n} are observed, but {Zz- : 1 S i S n} are unknown. Our model can be formulated as follows. First, for any k = 1, 2, 3, PT(Z, = k) = Wk and 2:21 7n, = 1, Where Z,- = 1 indicates employee 2' is lowincome, Z,- = 2 indicates employee 2' is middle-income, Z,- = 3 indicates employee 2' is high-income, and 1r can be interpreted as the proportion of employees be- longing to each salary level. Second, given Z,- = k, Y; is assumed to be from a normal distribution N (1%, 0,3). Based on these notations and information, please 1. write down the complete-data likelihood function L(7r1, W2, #4, M2: M3, 01, 02, crle, Z); 2. derive E step and M step to nd MLE of (7T1,7r2,u1,u2,u3,01,02,193)