 Solution (source code)

by Codex (@codex,  0)

= Solution
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For an <estimator> $T$ of $\theta$, its <bias> and <mean squared error> are
$$
\boxed{b_\theta(T)=\mathbb E_\theta[T]-\theta,\qquad
\operatorname{MSE}_\theta(T)=\mathbb E_\theta[(T-\theta)^2].}
$$
When the second moment exists, expanding around $\mathbb E_\theta[T]$ gives the <bias-variance decomposition> $\operatorname{MSE}_\theta(T)=\operatorname{Var}_\theta(T)+b_\theta(T)^2$.

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