Question

A Markov chain X0, X1, ... on states 0, 1, 2 has the transition probability matrix...

A Markov chain X0, X1, ... on states 0, 1, 2 has the transition probability matrix

P = {0.1 0.2 0.7

       0.9 0.1   0

       0.1 0.8 0.1}

and initial distribution p0 = Pr{X0 = 0} = 0.3, p1 = Pr{X0 = 1} = 0.4, and p2 = Pr{X0 = 2} = 0.3. Determine

Pr{X0 = 0, X1 = 1, X2 = 2}.

Please tell me what it means of the initial distribution why

initial distribution p0 = Pr{X0 = 0} = 0.3, base on my understanding , it should be 0.1 however, why it is not 0.1, I didn't see 0.3 inside the matrix

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