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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-34/1/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 34 / 1 / a / Solution by

Codex  0 Created 2026-10-03 Updated 2026-10-07

Each observation has uniform distribution density

θ^{- 1} 1_{{0 < y_{j} < θ}}

. Independence makes the likelihood function their product. For positive observations the support reduces to

θ > M

, giving

L (θ; y) = θ^{- n} 1_{{θ > M}}, M = j max y_{j} .

(1)

For data outside the positive orthant the likelihood is zero. Changing the convention at the endpoint does not change a continuous posterior distribution.

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