Solution
= 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
$$
\boxed{R(\theta,\widehat\theta_{a,b})
=\frac{a^2}{n}+\bigl((a-1)\theta+b\bigr)^2}.
$$
= 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
$$
\boxed{R(\theta,\widehat\theta_{a,b})
=\frac{a^2}{n}+\bigl((a-1)\theta+b\bigr)^2}.
$$