Example 29: The Xn;n = 1, 2, 3, .. having three states 1, 2 and 3 is transition probability matrix of a Markov chain 0.1 0.5 0.4 P = 0.6 0.2 0.2 0.3 0.4 0.3 and the initial distribution is p = (0.7, 0.2, 0.1). Find (i) P{X2 =3}, (ii) P{ X3 = 2, X2 = 3, X1 = 3, Xo = 2}

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 34E
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Example 29: The transition probability matrix of a
|Xn;n = 1, 2, 3, .... having three states 1, 2 and 3 is
Markov chain
0.1 0.5 0.4
P = 0.6 0.2 0.2
0.3 0.4 0.3
and the initial distribution is p0 = (0.7, 0.2, 0.1).
Find (i) P{X2 = 3, (ii) P{ X3 = 2, X2 = 3, X1 = 3, X, = 2 }
%3D
Transcribed Image Text:Example 29: The transition probability matrix of a |Xn;n = 1, 2, 3, .... having three states 1, 2 and 3 is Markov chain 0.1 0.5 0.4 P = 0.6 0.2 0.2 0.3 0.4 0.3 and the initial distribution is p0 = (0.7, 0.2, 0.1). Find (i) P{X2 = 3, (ii) P{ X3 = 2, X2 = 3, X1 = 3, X, = 2 } %3D
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