 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2010/m/2/a/solution

π = (π_{1}, π_{2})

satisfies

π P = π

and

π_{1} + π_{2} = 1

. The first equation reduces to the balance relation

a π_{1} = b π_{2}

. Since

a, b > 0

, normalization gives the unique solution

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

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