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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/13k/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 13K / a / Solution by

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

P_{λ} (Y = y) = \frac{1}{y !} exp {y lo g λ - λ} .

(1)

Thus this is an exponential family with natural parameter $θ = lo g λ$ , statistic $T (y) = y$ , base measure $1/ y!$ , and cumulant $A (θ) = e^{θ}$ .

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