What is the justification of using taylor approximations inside expectation operators? – stats.stackexchange.com

What is the justification of using taylor approximations inside expectation operators? – stats.stackexchange.com

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I sometimes see people use taylor approximation as follows: $$E(e^x)\approx E(1+x)$$ I know that the taylor approximation works for $$e^x \approx 1+x$$ But it is not clear to me that we can do the ...

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