2. Consider a Markov chain (✗n) with state space S = {1, 2, 3, 4, 5} and transition matrix 0.5 0.5 0 0 0 0.4 0.6 0 0 0 P = 0 0.3 0.3 0.4 0 0 0 0 0.6 0.4 0 0 0 0.6 0.4 One stationary distribution for this Markov chain is (4, 5,0,0,0). stationary distil Suppose the Markov chain (✗n) is started from the initial distribution λ = (0.1 0 0.7 0.2 0). What are the limiting probabilities lim→∞ P(X = i) for each i Є S? another [5] [4]
2. Consider a Markov chain (✗n) with state space S = {1, 2, 3, 4, 5} and transition matrix 0.5 0.5 0 0 0 0.4 0.6 0 0 0 P = 0 0.3 0.3 0.4 0 0 0 0 0.6 0.4 0 0 0 0.6 0.4 One stationary distribution for this Markov chain is (4, 5,0,0,0). stationary distil Suppose the Markov chain (✗n) is started from the initial distribution λ = (0.1 0 0.7 0.2 0). What are the limiting probabilities lim→∞ P(X = i) for each i Є S? another [5] [4]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![2. Consider a Markov chain (✗n) with state space S
=
{1, 2, 3, 4, 5} and transition matrix
0.5 0.5 0
0
0
0.4 0.6 0
0
0
P =
0
0.3 0.3
0.4 0
0
0 0
0.6 0.4
0
0
0 0.6 0.4
One stationary distribution for this Markov chain is (4, 5,0,0,0).
stationary distil
Suppose the Markov chain (✗n) is started from the initial distribution
λ = (0.1 0 0.7 0.2 0).
What are the limiting probabilities lim→∞ P(X = i) for each i Є S?
another
[5]
[4]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3011c556-643e-4a01-b0e0-55d8cf24eddf%2F64735066-2e2d-4e23-948f-961c8c7f86c2%2Fced76id_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider a Markov chain (✗n) with state space S
=
{1, 2, 3, 4, 5} and transition matrix
0.5 0.5 0
0
0
0.4 0.6 0
0
0
P =
0
0.3 0.3
0.4 0
0
0 0
0.6 0.4
0
0
0 0.6 0.4
One stationary distribution for this Markov chain is (4, 5,0,0,0).
stationary distil
Suppose the Markov chain (✗n) is started from the initial distribution
λ = (0.1 0 0.7 0.2 0).
What are the limiting probabilities lim→∞ P(X = i) for each i Є S?
another
[5]
[4]
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