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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-3/5j/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 5J / a / Solution by

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

Conditional independence makes the log-likelihood

ℓ (θ) = \sum_{i = 1}^{n} lo g f_{x_{i}} (Y_{i}; θ) .

A maximum-likelihood estimator is any

θ \in argmax_{θ \in Θ} ℓ (θ)

. If the model has

q

fitted real parameters, its Akaike information criterion is

AIC = - 2 ℓ (θ) + 2 q .

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