Question: Please answer the question below and don't copy others, thank you! Problem 4. You play a game in which each turn you have a chance

Please answer the question below and don't copy others, thank you!

Problem 4. You play a game in which each turn you have a chance to win $2. If you have at least 552 then you Win $2 with probability 1j3, and you lose $2 with probability 233. If you have $0 then you win $2 with probability III}... and nothing happens with probability 233. You start off with $4 and play forever. (a) (10p) Model this situation using a Markov chain, and show that there exists a 1mique stationary distribution for this litlarlcov chain. {h} (10p) Determine the probability that you will have exactly $101] at least once during this game

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