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4. The gambler bets $1 per game and either wins or loses each game. The gambler is ruined if he/she reaches state 0 and the gambler stops playing if he/she reaches state N, a winner. The probability of winning is p > 0 and the probability of losing is q> 0, p + q = 1 (that is P₁,i+1 = p and Pi+1,i = q. In addition Poo = 1 = PNN- a. Write the stochastic matrix P correspond to this case? What is the state space? b. Identify the communicating classes and classify the Markov chain as reducible or irreducible, closed or not closed? c. Identify each states as transient of recurrent?

4. The gambler bets $1 per game and either wins or loses each game. The gambler is ruined if he/she reaches state 0 and the gambler stops playing if he/she reaches state N, a winner. The probability of winning is p > 0 and the probability of losing is q> 0, p + q = 1 (that is P₁,i+1 = p and Pi+1,i = q. In addition Poo = 1 = PNN- a. Write the stochastic matrix P correspond to this case? What is the state space? b. Identify the communicating classes and classify the Markov chain as reducible or irreducible, closed or not closed? c. Identify each states as transient of recurrent?

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. The gambler bets $1 per game and either wins or loses each game. The gambler is ruined if he/she reaches state 0 and the gambler stops playing if he/she reaches state N, a winner. The probability of winning is p > 0 and the probability of losing is q> 0, p + q = 1 (that is Pi,i+1 = p and Pi+1,i q. In addition Poo = 1 = PNN. a. Write the stochastic matrix P correspond to this case? What is the state space? b. Identify the communicating classes and classify the Markov chain as reducible or irreducible, closed or not closed? c. Identify each states as transient of recurrent?
Transcribed Image Text:4. The gambler bets $1 per game and either wins or loses each game. The gambler is ruined if he/she reaches state 0 and the gambler stops playing if he/she reaches state N, a winner. The probability of winning is p > 0 and the probability of losing is q> 0, p + q = 1 (that is Pi,i+1 = p and Pi+1,i q. In addition Poo = 1 = PNN. a. Write the stochastic matrix P correspond to this case? What is the state space? b. Identify the communicating classes and classify the Markov chain as reducible or irreducible, closed or not closed? c. Identify each states as transient of recurrent?
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