 Solution

ID: past-exam-of-the-probability-course-of-the-university-of-oxford/2023/3/a/i/solution

S

is precisely a row vector satisfying

π_{i} \geq 0 (i \in S), i \in S \sum π_{i} = 1.

p_{i, j} \geq 0 (i, j \in S), j \in S \sum p_{i, j} = 1 (i \in S) .

Every row therefore gives the conditional probability distribution of the next state given the present state. These conditions do not require

π

P

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