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Also see
MML
Stein's Lemma:
E[ g(x) * (x-μ) ] = E[ g'(x) ]
where g(x) is an everywhere differentiable function of x, and μ is a location parameter (--Daniel).
 
If h is a "smooth" function of x, and E[X]=μ & variance[X]=ν, the expectation
E[ h(x) ]
= E[ h(μ) + (x-μ) . h'(μ) + (x-μ)2/2 . h''(μ) + ... ]   --by Taylor expansion about μ
= h(μ) + (ν/2)h''(μ) + ...
which may come in useful for approximating Fisher information, etc. (--DS).
 
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