 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-1/6h/c/solution

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

For

σ > 0

, the density is

p_{σ} (x) = \frac{1}{2 π σ} exp (- \frac{x ^{2}}{2 σ ^{2}}) = g_{σ} (∣ x ∣),

∣ X ∣

is sufficient.

Moreover,

\frac{p _{σ} ( x )}{p _{σ} ( y )} = exp (- \frac{x ^{2} - y ^{2}}{2 σ ^{2}})

is independent of

σ

exactly when

x^{2} = y^{2}

, equivalently

∣ x ∣ = ∣ y ∣

∣ X ∣ is minimal sufficient .

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