Stein's Lemma

$\mathbb{E}[g(X)(X-\mu )]={\sigma }^2\mathbb{E}[g^{\prime }(X)]$ where:

• $X$ is a Random variable
• $\mu :=\mathbb{E}[X]$
• ${\sigma }^2:=\mathbb{E}[(X-\mu {)}^2]$
• $g:\mathbb{R}\to \mathbb{R}$ a differentiable function with finite moments.