Question: Question 2(10 points) Let Xn be a Markov chain with the following transition matrix O N/ O Suppose the initial state Xo has distribution 7

Question 2(10 points) Let Xn be a Markov chain with the following transition matrix O N/ O Suppose the initial state Xo has distribution 7 = :). 1. Draw the transition diagram. 2. Find the stationary probability distribution. 3. Find a vector of probability to describe the unconditional probability distribution of X4 4. Calculate P(X1 = 3, X2 = 1 | Xo = 1) 5. Calculate P(Xo = 1, X1 = 3, X2 = 1) 6. Calculate P(Xo = 3, X2 = 3, X4 = 1) [Hint: consider two steps transition]

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