Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 28L / b / iii

Given $X=x$, the posterior expected loss from reporting $d$ isThis is a strictly convex quadratic in $d$ whenever the conditional inverse moment is finite and positive. Differentiating with respect to $d$ givesso the Bayes estimator under reciprocal weighted quadratic loss is