Four white and four black balls are distributed in two urns in such a way that each contains four balls. We say that the system is in state i,i = 0,1,2,3,4 , if the first urn contains i white balls. At each step, we draw one ball from each urn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Let Xn denote the state of the system after the nth step. Explain why {Xn, n = 1, 2, 3, . . .} is a Markov chain and calculate its transition matrix. 1. Four white and four black balls are distributed in two urns in such away that each contains four balls. We say that the system is in statei, i = 0, 1, 2, 3, 4 , if the first urn contains i white balls. At each step,we draw one ball from each urn and place the ball drawn from thefirst urn into the second, and conversely with the ball from the secondurn. Let X, denote the state of the system after the nth step. Explainwhy {Xn,n = 1, 2, 3, . . } is a Markov chain and calculate its transitionmatrix.

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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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Four white and four black balls are distributed in two urns in such a way that each contains four balls. We say that the system is in state i,i = 0,1,2,3,4 , if the first urn contains i white balls. At each step, we draw one ball from each urn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Let Xn denote the state of the system after the nth step. Explain why {Xn, n = 1, 2, 3, . . .} is a Markov chain and calculate its transition matrix.