 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-34/3/a/solution

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

p (y_{i} ∣ p_{i}, n_{i}) = \frac{n _{i} !}{\prod _{k = 1}^{K} y _{ik} !} k = 1 \prod K p_{ik}^{y_{ik}}, y_{ik} \in {0, 1, \dots}, k \sum y_{ik} = n_{i} .

It is zero outside this count simplex. The multinomial coefficient counts the individual category sequences giving the same aggregate counts; the probability vector satisfies

\sum_{k} p_{ik} = 1

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