Q6 At all times, an urn contains N balls- some white balls and some black balls. At each stage, a coin having probability p, 0 0} a Markov Chain? If so, explain why. Q6(ii.) Compute the transition probabilities Pij. (Hint: At some stage, suppose there are i white balls (and N – i black balls). Think how you can get i or i – 1 or i +1 white balls in the next stage.) Q6(iii.) Let N = 2. Then the states are 0, 1, 2 and the transition probability matrix is given by P р Find the proportion of the time in each state.

Q6 At all times, an urn contains N balls- some white balls and some black balls. At each stage, a coin having probability p, 0 0} a Markov Chain? If so, explain why. Q6(ii.) Compute the transition probabilities Pij. (Hint: At some stage, suppose there are i white balls (and N – i black balls). Think how you can get i or i – 1 or i +1 white balls in the next stage.) Q6(iii.) Let N = 2. Then the states are 0, 1, 2 and the transition probability matrix is given by P р Find the proportion of the time in each state.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 9EQ

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