0 0 0 are steady-state vectors 0 3/5 0 2/5 for the Markov chain below. If the chain is equally likely to begin in each of the states, what is the probability of being in state 2 after many steps? Show that q₁ = P= 3/11 3/11 5/11 and 9₂5 = 1 2 3 1/3 1/4 1/4 1/3 1/4 1/3 1/2 1/4 1/2 4 0 0 0 5 1 0 0 2 0 3 The vector q, is a steady-state vector because ap pq₁ q/p-1 p-¹a₁ simplified fraction for each

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Chapter1: Combinatorial Analysis
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Show that q₁ =
0
0
0
0
3/5
0
2/5
for the Markov chain below. If the chain is equally likely to begin in
each of the states, what is the probability of being in state 2 after
many steps?
P=
1
1/3
3
1/4
1/3 1/4
1/4
1/3 1/2 1/2
0
0
0
3/11
3/11
5/11 and 92
2
1/4
0
4
0
0
0
=
5
are steady-state vectors
0 1
0 2
0 3
2/3
1/2
4
00 1/3 1/2 5
The vector q, is a steady-state vector because
q/p
Pq₁
9 P-1
P¹q₁
simplified fraction for each
Transcribed Image Text:Show that q₁ = 0 0 0 0 3/5 0 2/5 for the Markov chain below. If the chain is equally likely to begin in each of the states, what is the probability of being in state 2 after many steps? P= 1 1/3 3 1/4 1/3 1/4 1/4 1/3 1/2 1/2 0 0 0 3/11 3/11 5/11 and 92 2 1/4 0 4 0 0 0 = 5 are steady-state vectors 0 1 0 2 0 3 2/3 1/2 4 00 1/3 1/2 5 The vector q, is a steady-state vector because q/p Pq₁ 9 P-1 P¹q₁ simplified fraction for each
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