 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-2/29k/a/solution

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

Since

\overline{X}_{n} \sim N (θ, 1/ n)

, the estimator has variance

a^{2} / n

and bias

(a - 1) θ + b

. Its quadratic risk function is

R (θ, θ_{a, b}) = \frac{a ^{2}}{n} + ((a - 1) θ + b)^{2} .

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