 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2010/m/m5/c/solution

Conditioning on the initial state gives

P (X_{n} = i) = j \in S \sum λ_{j} (P^{n})_{ji} = (λ P^{n})_{i} .

Thus the row-vector distribution at time

n

λ P^{n}

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