Question

Please help with Markov Chains! Please help finding the limiting probababilities. Thank you! I don’t need part A

1. A fair die is rolled repeatedly. Let X, denote the largest score after n rolls, n 1,2..... For example. if the outomes of the finst fve rols are: 4, 4, 2,6and 3, then and X6 te the largest score atter n FoS 1,2,..) Markov chain? If so, determine the transition probability matrix. (10 points)

Answer 1

Since the state, X_n is the largest number rolled in n rolls, the set of states S ={1,2,3,4,5,6}. The probability of the largest number rolled in the first (n+1) trials is only dependent on what the largest number that was rolled in the first n trials. This satisfies the Markov property. The transition probabilities are given by:

0.2-61-6

TRANSITION PROBABILITY MATRIX IS:

-61-61-61-61-60-6 161-61-61-656 0 16161646 0 0 161626000 1600000

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