Question no. 42 Suppose that [1/4 1/2 1/4 P= a 0 1-a

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
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Question no. 42
Suppose that
[1/4 1/2 1/4
0 1-a
ß 0 1-8]
P =
is the one-step transition probability matrix of a Markov chain with state
space (0, 1, 2}.
(a) For what values of a and 3 is the Markov chain irreducible?
(b) Suppose that a = 3 = 1/2. Compute, if they exist, the limiting probabil-
ities T,, for j = 0,1, 2.
(c) Suppose that Xo = 0. Compute the probability that the process will (i)
visit state 1 before state 2 and (ii) return to (or stay in) state 0 before visiting
state 2.
%3D
Transcribed Image Text:Urgent! Question no. 42 Suppose that [1/4 1/2 1/4 0 1-a ß 0 1-8] P = is the one-step transition probability matrix of a Markov chain with state space (0, 1, 2}. (a) For what values of a and 3 is the Markov chain irreducible? (b) Suppose that a = 3 = 1/2. Compute, if they exist, the limiting probabil- ities T,, for j = 0,1, 2. (c) Suppose that Xo = 0. Compute the probability that the process will (i) visit state 1 before state 2 and (ii) return to (or stay in) state 0 before visiting state 2. %3D
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