I did a quick search and found this answer When can we interchange the derivative with an expectation? (the top answer) but I think it applies not in the general case that I am referring to. I want to compute the hessian of $J(w) := \mathbb{E}_{p}[(w^T x - t)^2]$ with regard to $w$ and know that I can apply the second derivative operator and "switch its application order" with that of the expected value operator. Can someone tell me why this is possible? Thanks!
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