Problem 3 You have in your pocket. You are given a coin that lands heads with pr

Question

Problem 3 You have in your pocket. You are given a coin that lands heads with probability p. Every minute you toss the coin once. If it is heads you gain an extra $1. If it is tails you lose a $1. If you reach $0 then you will have $0 for the rest of the game, regardless of what your coin comes up. The (small) House has $5. So if you reach $8 you will have $8 for the rest of the game regardless of what your coin lands. Is this a. Markov chain? Why or why not? If it is, write its transition matrix.

Explanation / Answer

This is not a markov chain. Consider $0,$1 .....$8 to be the different states. It is clearly given that once you reach the stage $8 then you can't go anywhere else, which is not in the case of Markov chain.

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