 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/13k/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Expanding

\sum (X_{i} - \overset{ˉ}{X}) (Y_{i} - \overset{ˉ}{Y}) = \sum X_{i} Y_{i} - n \overset{ˉ}{X} \overset{ˉ}{Y}

and taking expectations gives

(n - 1) (E [X Y] - EX, E Y)

n - 1

proves unbiasedness.

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