the related files are not important for the first two question. I want to know how to derive the log-likelihoodafter adding another distribution into the mixture model. What is the probability for X301,...,X400?

Let X1, . . . ,Xgoo and X301, . . . ,X400 denote the 300 observations from assignmenthrob2 . txt and the 100 observations from assignment2_prob3.txt, respectively. We assume the ob servations X1, . . . , X400 are independent to each other. We model X1, . . . ,Xgoo (from assignment2_prob2 . txt) using the mixture of three binomial distributions [as we did in the problem 2), but we model X301, . . . ,X400 (from assigmentlprob3.txt) using one of the three binomial distributions. Specifically, for 1' = 1, . . . ,300, Xi follows this mixture model: Z5 M categorical (7r1,7r2,1 7T1 7T2), X|Z = l N Binomial(20,p1), Xi|Z = 2 ~ Binomial[20,p2), Xi|Zi = 3 N Binomial(20,p3), and for i = 301, . . . , 400, Xi ~ Binomial(20,p1). We aim to obtain MLE of parameters 6 = (m, 7r2, 101,132,303) using the EM algorithm. (a) (5 marks) Let X = (X1,...,X400) and Z = (21,...,Z300). Derive the expectation of the complete loglikelihood, Q(6, 90) = E2|X,90[10g(P(X, Z|9))]. (b) (5 marks) Derive Estep and M-step of the EM algorithm