 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/5l/a/solution

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

Conditionally on

x_{i}

P (Z_{i} = 1 ∣ x_{i}) = Φ (\frac{μ + x _{i}^{T} β - τ}{σ}) .

η_{i} = α + x_{i}^{T} γ, α = \frac{μ - τ}{σ}, γ = \frac{β}{σ} .

Fit

(α, γ)

by maximum likelihood for Bernoulli observations, then recover

μ = τ + σ α, β = σ γ .

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