 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-1/13k/d/solution

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

For

p = 1

, part (c) gives

Var (β (Σ)) \sim \frac{σ ^{2}}{n E [ X _{1}^{2} / v ( X _{1} )]},

Var (β (I)) \sim \frac{σ ^{2} E [ v ( X _{1} ) X _{1}^{2} ]}{n ( E [ X _{1}^{2} ] ) ^{2}} .

Consequently

ρ = \frac{( E [ X _{1}^{2} ] ) ^{2}}{E [ X _{1}^{2} / v ( X _{1} )] E [ v ( X _{1} ) X _{1}^{2} ]} .

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