EM and Information Suppose we have a bunch of coins C consisting two kinds of coins. Mathematically, it obeys a mixed Bernoulli distribution: XNF =1rF1+[117)Fg where 11' 6 [0,1] and F1 : Ber(p1), F2 : Ber(p2). That's to say, the kind of the coin is determined by a latent variable Z = 1 or Z = 2. Here Ber-(p) means the coin gives 1 (head) with probability p and gives '1] [tail] with probability 1 p. We initialize parameters p1 = %, P2 = g and 11' = %. Now, we draw 4 coins X1, X2, X3, X4 independently from C and have 3 independent trials for each of them. The result shows: Coins X1 X2 X3 X4 Trail 1 1 (l D 1 Trail 2 1 1 1 U Trail 3 G 1 D 1 a Use EM algorithm for one step, we update F = F 1 = 1,112 = 3,1: = l to F' ',p',7r' . Write a 3 2 1 2 down your EM algorithm and show the value of pi, p5, rt