 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/29l/c/solution

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

The likelihood is

e^{- \sum_{i} X_{i} + n θ} 1_{{θ \leq X_{(1)}}},

θ_{n} = X_{(1)}

. Regular asymptotics fail because the support

[θ, \infty)

depends on

θ

and the likelihood maximum lies on its boundary.

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