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Hello,

have a stats question I am hoping you guys can help with. The expectation of a function g of a random variable X is:

E[g(X)] = [tex]\int^{\infty}_{-\infty}[/tex] g(x)f_{x}(x)dx

where f_{x}is the pdf of X. For example, the particular expectation I am considering right now is:

E[g(X)] = [tex]\int^{-\infty}_{\infty}\frac{1}{1+ax^{2}}\cdot \frac{1}{\sqrt{2\pi}}[/tex][tex]e^{-x^{2} / 2}dx[/tex]

this form of integral (i.e. containing that particular e term) must happen often whenever one takes the expectation of a function which depends on a normal random variable. In general, what is the best approach to solve such integrals in closed form here? Integration by parts? I know that the normal curve itself must be integrated using a "trick" such as switching to polar coordinates. Integration by parts might help me isolate the e term to do so, but actually in this case I am not making much progress using that method because the other (first) term has x in the denominator. Any thoughts as to a general approach and/or to this specific problem are much appreciated. thanks!

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# Integration help for expectation of a function of a random variable

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