Question

Consider a Markov Chain on {1,2,3} with the given transition matrix P. Use two methods to find the probability that in the lo

Calculate P100 p100 0.20833 0.20833 0.20833 0.58333 0.58333 0.58333 0.20833 0.20833 0.20833 (Type an integer or decimal for e

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Answer #1

Code:

A = [1/3 1/4 0;1/3 1/2 1;1/3 1/4 0]
B = A^100
C = rats(B)

Output:

A =

    0.3333    0.2500         0
    0.3333    0.5000    1.0000
    0.3333    0.2500         0


B =

    0.2143    0.2143    0.2143
    0.5714    0.5714    0.5714
    0.2143    0.2143    0.2143


C =

3×42 char array

    '      3/14          3/14          3/14    '
    '      4/7           4/7           4/7     '
    '      3/14          3/14          3/14    '

C gives you the P^100 in exact rational form.

Also by eigenvalue decomposition note that the steady-state vector is (3,8,3)^t.

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