 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2010/m/m2/a/solution

(π_{1}, π_{2})

π P = π

reduces to

a π_{1} = b π_{2}

. Together with

π_{1} + π_{2} = 1

, this gives

π = (\frac{b}{a + b}, \frac{a}{a + b}) .

The positive transition probabilities make the two states communicate, so the stationary distribution is unique.

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