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

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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 1 (84.96 KiB) Viewed 25 times

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(Xo = 0) = 0.15, P(Xo = 1) = 0.5, P(Xo = 2) = 0.25 and P(Xo = 3) = 0.1. (a) Find E[X3|Xo = 2]. [4 marks] (b) Determine the joint distribution of Xo and X1. [4 marks] (C) Find the periodicity of each state. [4 marks] (d) Suppose that Xo 0. Find the mean time to reach state 1. [4 marks] (e) Suppose that Xo = 0. Find the probability that the Markov chain will ever visit state 1. (4 marks] -