 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-4/13j/i/solution

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

Let

Y_{i}

be the first team's goal count in match

i

, let

x_{i}^{T}

be row

i

of the design matrix, and let

β

Y_{i}

Y_{i} \sim Pois (μ_{i}), lo g μ_{i} = x_{i}^{T} β .

The likelihood function maximized by glm is therefore

L (β; y) = i = 1 \prod 64 \frac{μ _{i}^{y_{i}} e ^{- μ_{i}}}{y _{i} !} = i = 1 \prod 64 \frac{exp { y _{i} x _{i}^{T} β - e ^{x_{i}^{T} β} }}{y _{i} !} .

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