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**Notation**: I was schooled in the statistician’s notation
\(\mathbb{E}_{p(x)}[f(x)]\) to denote the expected value of \(f(x)\) with
respect to the density/mass \(p(x)\). More recently, I’ve picked up the physicist
notation \(\langle f(x) \rangle_x\). I may move interchangably between the two.