 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ib/paper-4/17h/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The unrestricted maximum-likelihood estimates are

(\overset{ˉ}{X}, \overset{ˉ}{Y})

, while the null fixes both means at zero. Hence

- 2 lo g Λ = m \overset{ˉ}{X}^{2} + n \overset{ˉ}{Y}^{2} .

Under the null this is

χ_{2}^{2}

, so the size-

α

m \overset{ˉ}{X}^{2} + n \overset{ˉ}{Y}^{2} > F_{2}^{- 1} (1 - α) .

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