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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.

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
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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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
Transcribed Image Text: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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