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Suppose we have a board with four squares marked 1, 2, 3, 4 as in the picture: 3 We play a game where a counter is placed on one of the squares and we move it to an adjacent square with probability given by the following table: Current position can move to these positions with this probability 2 with probability 4, 3 with probability I with probability , 4 with probability I with probability 4, 4 with probability 2 with probability , 3 with probability 2 3 Let x be a vector such that r, is the probability that the counter is on square i. (a) Write down a stochastic matrix A such that vector Ax gives the probability for the position of the counter after one move. (b) Suppose we begin the game by placing the counter on square num- ber 1. Use your matrix from part (a) to calculate the probability it is on square I after two moves.

Suppose we have a board with four squares marked 1, 2, 3, 4 as in the picture: 3 We play a game where a counter is placed on one of the squares and we move it to an adjacent square with probability given by the following table: Current position can move to these positions with this probability 2 with probability 4, 3 with probability I with probability , 4 with probability I with probability 4, 4 with probability 2 with probability , 3 with probability 2 3 Let x be a vector such that r, is the probability that the counter is on square i. (a) Write down a stochastic matrix A such that vector Ax gives the probability for the position of the counter after one move. (b) Suppose we begin the game by placing the counter on square num- ber 1. Use your matrix from part (a) to calculate the probability it is on square I after two moves.

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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Suppose we have a board with four squares marked 1, 2, 3, 4 as in the picture: 3 We play a game where a counter is placed on one of the squares and we move it to an adjacent square with probability given by the following table: Current position can move to these positions with this probability 2 with probability 4, 3 with probability I with probability , 4 with probability I with probability 4, 4 with probability 2 with probability , 3 with probability 2 3 4 Let x be a vector such that r, is the probability that the counter is on square i. (a) Write down a stochastic matrix A such that vector Ax gives the probability for the position of the counter after one move. (b) Suppose we begin the game by placing the counter on square num- ber 1. Use your matrix from part (a) to calculate the probability it is on square I after two moves.
Transcribed Image Text:Suppose we have a board with four squares marked 1, 2, 3, 4 as in the picture: 3 We play a game where a counter is placed on one of the squares and we move it to an adjacent square with probability given by the following table: Current position can move to these positions with this probability 2 with probability 4, 3 with probability I with probability , 4 with probability I with probability 4, 4 with probability 2 with probability , 3 with probability 2 3 4 Let x be a vector such that r, is the probability that the counter is on square i. (a) Write down a stochastic matrix A such that vector Ax gives the probability for the position of the counter after one move. (b) Suppose we begin the game by placing the counter on square num- ber 1. Use your matrix from part (a) to calculate the probability it is on square I after two moves.
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