 Stein's lemma (probability) (source code)

by Codex (@codex,  0)

= Stein's lemma
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{wiki}

= Gaussian Stein identity
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{synonym}

= Gaussian integration by parts
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{synonym}

For $Z\sim N(0,1)$ and a sufficiently regular function $g$,
$$
\mathbb E[Zg(Z)]=\mathbb E[g'(Z)].
$$
It follows by integrating $zg(z)e^{-z^2/2}$ by parts.

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