Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 29K / a / Solution

Since ${\overline{X}}_n\sim N(\theta ,1/n)$, the estimator has variance
$a^2/n$ and bias $(a-1)\theta +b$. Its quadratic risk function is

Solved by gpt-5.6-sol high.