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4. Suppose that Joe is playing the following version of the gambler's ruin problem. He starts with $50, and plays the game (in which he wins or loses $1 with probability 1/2-1/2) until he reaches $200 or loses all his money. Whenever he loses all his money, he goes to his bank, borrows $50 again and starts playing again. If he reaches $200 then he stops playing forever. (a) Model the game as a Markov chain, describing the transition probability function. (b) Is it true that with probability one Joe will stop playing at some point? (I.e. that he will hit $200.)

4. Suppose that Joe is playing the following version of the gambler's ruin problem. He starts with $50, and plays the game (in which he wins or loses $1 with probability 1/2-1/2) until he reaches $200 or loses all his money. Whenever he loses all his money, he goes to his bank, borrows $50 again and starts playing again. If he reaches $200 then he stops playing forever. (a) Model the game as a Markov chain, describing the transition probability function. (b) Is it true that with probability one Joe will stop playing at some point? (I.e. that he will hit $200.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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4. Suppose that Joe is playing the following version of the gambler's ruin problem. He starts with $50, and plays the game (in which he wins or loses $1 with probability 1/2 - 1/2) until he reaches $200 or loses all his money. Whenever he loses all his money, he goes to his bank, borrows $50 again and starts playing again. If he reaches $200 then he stops playing forever. (a) Model the game as a Markov chain, describing the transition probability function. (b) Is it true that with probability one Joe will stop playing at some point? (I.e. that he will hit $200.)
Transcribed Image Text:4. Suppose that Joe is playing the following version of the gambler's ruin problem. He starts with $50, and plays the game (in which he wins or loses $1 with probability 1/2 - 1/2) until he reaches $200 or loses all his money. Whenever he loses all his money, he goes to his bank, borrows $50 again and starts playing again. If he reaches $200 then he stops playing forever. (a) Model the game as a Markov chain, describing the transition probability function. (b) Is it true that with probability one Joe will stop playing at some point? (I.e. that he will hit $200.)
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