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Two gamblers play the following game: A fair coin is flipped; if the outcome is head, player A pays player B $1, and if the outcome is tail, player B pays player A $1. The game is continued until one of the players goes broke. Suppose that initially player A has $1 and player B has $2. (a). Sketch the state transition diagram for this Markov chain. Find the one-step transition Define the state Xn as the number of dollars held by player A after n trials. probability matrix P. (b) Identify the classes in this Markov chain, classify them as recurrent or transient.

Two gamblers play the following game: A fair coin is flipped; if the outcome is head, player A pays player B $1, and if the outcome is tail, player B pays player A $1. The game is continued until one of the players goes broke. Suppose that initially player A has $1 and player B has $2. (a). Sketch the state transition diagram for this Markov chain. Find the one-step transition Define the state Xn as the number of dollars held by player A after n trials. probability matrix P. (b) Identify the classes in this Markov chain, classify them as recurrent or transient.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Two gamblers play the following game: A fair coin is flipped; if the outcome is head, player A pays player B $1, and if the outcome is tail, player B pays player A $1. The game is continued until one of the players goes broke. Suppose that initially player A has $1 and player B has $2. (a) Define the state X, as the number of dollars held by player A after n trials. Sketch the state transition diagram for this Markov chain. Find the one-step transition probability matrix P. (b) (c) Identify the classes in this Markov chain, classify them as recurrent or transient. What is the probability that player A will win the game in less than 5 trials?
Transcribed Image Text:Two gamblers play the following game: A fair coin is flipped; if the outcome is head, player A pays player B $1, and if the outcome is tail, player B pays player A $1. The game is continued until one of the players goes broke. Suppose that initially player A has $1 and player B has $2. (a) Define the state X, as the number of dollars held by player A after n trials. Sketch the state transition diagram for this Markov chain. Find the one-step transition probability matrix P. (b) (c) Identify the classes in this Markov chain, classify them as recurrent or transient. What is the probability that player A will win the game in less than 5 trials?
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