. 1. Consider a Markov chain {Xt} with states 0, 1, 2, and 3, whose transition probability matrix is 0.2 0.1 0.4 0.3 1 0

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1 Consider A Markov Chain Xt With States 0 1 2 And 3 Whose Transition Probability Matrix Is 0 2 0 1 0 4 0 3 1 0 1 (114.65 KiB) Viewed 33 times

. 1. Consider a Markov chain {Xt} with states 0, 1, 2, and 3, whose transition probability matrix is 0.2 0.1 0.4 0.3 1 0 0 0 P= = 0.25 0.35 0.1 0.3 0 0 1 0 = = = = The initial distribution is P(X0 = 0) = 0.15, P(X) = 1) = 0.5, P(Xo = 2) = 0.25 and P(X) = 3) = 0.1. = = (a) Find E[X3|Xo = 2]. = (4 marks] (b) Determine the joint distribution of X, and X1. [4 marks] (4 marks (c) Find the periodicity of each state. (d) Suppose that X0 = 0. Find the mean time to reach state 1. [4 marks (e) Suppose that X0 = 0. Find the probability that the Markov chain will ever visit state 1. (4 marks]