Suppose we have a bunch of coins C consisting three kinds of coins. Mathematically, it obeys a mixed Bernoulli distribution: X N F = 751171 +2F2 +(17Z'17Z'2)F3 where 7r 6 [0, 1], and F1 = Ber(p1), F2 = Ber(p2), F3 = Ber(p3). That is to say, each coin belongs to F1, F2 or F3. Here Ber(p) means the coin gives 1 (head) with probability p and gives 0 (tail) with probability 1 p. We initialized parameters p1 = %,p2 = g, [)3 = %, 751 = %, 71'2 = % Now, we draw 3 coins X1, X2, X3 independently from C and have 6 independent trials for each of them. The result shows: X2 X3 1 1 1 1 0 1 1 1 0 1 0 0 E2 = %) to 2.2.1. Use EM algorithm for one step, we update F = F(p1 = %, P2 = %, p3 = %,7r1 = %, F/(p'l, P12, pg, 7:1, ). Write down your EM algorithm and show the value of 12,1, 1);, pg, 7:1, 7%. (Round the answer to three decimal places.)