Xn is a Markov Chain with state-space E = {0, 1, 2}, and transition matrix
0.4 0.2 ?
P = 0.6 0.3 ?
0.5 0.3 ?
And initial probability vector a = [0.2, 0.3, ?]
a) What are the missing values (?) in the transition matrix an initial vector?
b) P(X1 = 0) =
c) P(X1 = 0|X0 = 2) =
d) P(X22 = 1|X20 = 2) =
e) E[X0] =
For the Markov Chain with state-space, initial vector, and transition matrix as defined above, discuss how we would calculate the following:
a) P(X1 = 0, X2 = 0, X3 = 1, X4 = 2|X0 = 2)
b) P(X2 = 2, X4 = 0, X5 = 1)
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