Give a proper mathematical explanation, not a statement. Don't give any AI-assisted results. Given the weighted quadratic loss function L(\theta, d)=w(\theta)(\theta-d)^2 \text { with } w(\theta)>0 \text { for all } \theta \in \Theta=\mathbb{R}

Determine $d_{\min }$ such that the posterior risk is minimized and interpret the solution. Hint: The order of differentiation and integration is interchangeable.