2.2 Let Xo. X1,... be a Markov chain with transition matrix12311/2 1/2)13(1/3 1/3 1/3)and initial distribution a = (1/2,0, 1/2). Find the following:(a) P(X, = 1|X¡ = 3)(b) P(X1 = 3, X2 = 1)(c) P(X1 = 3|X2 = 1)(d) P(X9 = 1|X1 = 3, X4 = 1,X7 = 2)%3D

a) Given that, Markow chain with transition matrix With initial distribution

Answered: 2.2 Let Xo. X,.. be a Markov chain with…

2.2 Let Xo. X,.. be a Markov chain with transition matrix 1 1/2 1/2 0 0 31/3 1/3 1/3) 1 2 and initial distribution a = (1/2,0, 1/2). Find the following: (a) P(X, = 1|X, = 3) (b) P(X1 = 3, X2 = 1) 3.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

2.2 Let Xo. X1,... be a Markov chain with transition matrix
1
2
3
1
1/2 1/2)
1
3(1/3 1/3 1/3)
and initial distribution a = (1/2,0, 1/2). Find the following:
(a) P(X, = 1|X¡ = 3)
(b) P(X1 = 3, X2 = 1)
(c) P(X1 = 3|X2 = 1)
(d) P(X9 = 1|X1 = 3, X4 = 1,X7 = 2)
%3D

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