Let X, be the Markov chain with state space Z and transition probabilityPa,z+1 = P, Pa,2-1 = 1- p,where p > 1/2. Assume X, = 0.(a) Let Y = min{Xo, X1,...}. What is the distribution of Y?(b) For positive integer k, let T = min{n : X, = k} and let e(k) = E[TR]. Explainwhy e(k) = ke(1).(c) Find e(1). Hint: part (b) might be helpful.(d) Use (c) to give another proof that e(1) = o if p = 1/2.

a) The value of Y represents the first time the Markov chain reaches its minimum value. In this…

Answered: Let X₁, be the Markov chain with state…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.

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