 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ia/paper-2/10f/c/solution

At most two of

X_{1} > X_{2}

X_{2} > X_{3}

, and

X_{3} > X_{1}

can hold in any outcome. Taking expectations gives

a_{12} + a_{23} + a_{31} \leq 2

, and hence $min {a_{12}, a_{23}, a_{31}} \leq 2/3$ .

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