Question: Consider a Markov chain with transition matrix 2 3 4 : 1/2 1/2 0 2/3 0 1/3 ZOO 3/4 0 . . . UIAWNA ...OROOO

Consider a Markov chain with transition matrix 2 3 4 : 1/2 1/2 0 2/3 0 1/3 ZOO 3/4 0 . . . UIAWNA ...OROOO P= 4/5 0 ...OOT 5/6 . . . . . . . . . . . . defined by i/(i + 1), if j = 1, Pi; = 1/(i+1), if j= i+ 1, 0, otherwise. (a) Does the chain have a stationary distribution? If yes, exhibit the distribution. If no, explain why. (b) Classify the states of the chain. (c) Repeat part (a) with the row entries of P switched. That is, let 1/(i + 1), if j = 1, Paj =i/(i+1), ifj= i+1, 0, otherwise

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