Problem 2. A player plays a game in which, during each round, he has a probability 0.45 of winning $1 and probability 0.55 of losing $1. These probabilities do not change from round to round, and the outcomes of rounds are independent. The game stops when either the player loses its money, or wins a fortune of $M. Assume M = 4, and the player starts the game with $2. %3! (a) Model the player's wealth as a Markov chain and construct the probability transition matrix. (b) What is the probability that the player goes broke after 2 rounds of play?

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Problem 2. A player plays a game in which, during each round, he has a probability 0.45 of winning
$1 and probability 0.55 of losing $1. These probabilities do not change from round to round, and
the outcomes of rounds are independent. The game stops when either the
player loses its money, or wins a fortune of $M. Assume M = 4, and the player starts the
game with $2.
(a) Model the player's wealth as a Markov chain and construct the probability transition
matrix.
(b) What is the probability that the player goes broke after 2 rounds of play?
Transcribed Image Text:Problem 2. A player plays a game in which, during each round, he has a probability 0.45 of winning $1 and probability 0.55 of losing $1. These probabilities do not change from round to round, and the outcomes of rounds are independent. The game stops when either the player loses its money, or wins a fortune of $M. Assume M = 4, and the player starts the game with $2. (a) Model the player's wealth as a Markov chain and construct the probability transition matrix. (b) What is the probability that the player goes broke after 2 rounds of play?
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