Three fair coins are tossed, and we let X1 denote the number of heads that appear. Those coins that were heads on the first trial (there were X1 of them) we pick up and toss again, and now we let X2 be the total number of tails, including those left from the ﬁrst toss. We toss again all coins showing tails, and let X3 be the resulting total number of heads, including those left from the previous toss. We continue the process. The pattern is, count heads, toss heads, count tails, toss tails, count heads, toss heads, etc., and X0 = 3. Then (Xn) is a Markov chain. What is its transition matrix?
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