I would like to know if the mean value of $\exp(-1/(ax^2)) $ when $x \sim N(0,1)$ and $a>0$ is a parameter is known.
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$\begingroup$ Could you perhaps formulate your question in a grammatically correct way? $\endgroup$– Stefan Kohl ♦Nov 6, 2014 at 21:28
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$\begingroup$ This is an elementary integral which is evaluated in the same way as the integral of $e^{-x^2}$. $\endgroup$– Alexandre EremenkoNov 6, 2014 at 21:51
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$\begingroup$ integrals.wolfram.com/index.jsp# $\endgroup$– Christian RemlingNov 6, 2014 at 22:32
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1 Answer
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$$e^{-{\sqrt{2/a}}}$$ is what Mathematica says...
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$\begingroup$ It should go to $1$ when $a\to\infty$. $\endgroup$ Nov 6, 2014 at 21:57