12.9 Consider the gamblers ruin problem where probability of winning is p = 1/2 and the initial...

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12.9 Consider the gambler’s ruin problem where probability of winning is p = 1/2 and the initial wealth is $100. Suppose the gambler stops if he reaches $200 or if he goes bankrupt. Let Xn the total wealth after n games. Show that Xn is a Markov chain, and write the probability transition matrix for the wealth. Classify the states in the chain as recurrent or transient. Does the chain have a stationary distribution? Is it unique?

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