Question 2 8 pts Consider the DTMC with state space {0, 1, 2, 3, 4} and...

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Question 2 8 pts Consider the DTMC with state space {0, 1, 2, 3, 4} and the following transition probability matrix: (0.1 0.2 0.3 0.2 0.2 0.4 0.1 0.1 0.1 0.3 P=0.2 0.3 0.1 0.2 0.2 0.3 0.1 0.1 0.1 0.4 0.1 0.2 0.5 0.1 0.1 1. Given Xo 1, find the expected value of X5 (provide three digits after the decimal point). 2. Given Xo = 1, find the probability that X, will ever visit State 2 for 1 n 5 (provide three digits after the decimal point). Bonus: Given Xo = 1, find the probability that the first time DTMC is in State 2 is at n = 5 (provide three digits after the decimal point). Question 2 8 pts Consider the DTMC with state space {0, 1, 2, 3, 4} and the following transition probability matrix: (0.1 0.2 0.3 0.2 0.2 0.4 0.1 0.1 0.1 0.3 P=0.2 0.3 0.1 0.2 0.2 0.3 0.1 0.1 0.1 0.4 0.1 0.2 0.5 0.1 0.1 1. Given Xo 1, find the expected value of X5 (provide three digits after the decimal point). 2. Given Xo = 1, find the probability that X, will ever visit State 2 for 1 n 5 (provide three digits after the decimal point). Bonus: Given Xo = 1, find the probability that the first time DTMC is in State 2 is at n = 5 (provide three digits after the decimal point).