I'm looking for the expected value of an exponential Gaussian(adsbygoogle = window.adsbygoogle || []).push({});

[itex]Y=\text{exp}(jX) \text{ where } X\text{~}N(\mu,\sigma^2) [/itex]

From wolframalpha, http://www.wolframalpha.com/input/?i=expected+value+of+exp%28j*x%29+where+x+is+gaussian

[itex]E[Y]=\text{exp}(j^2\sigma^2/2+j\mu)[/itex]

If I were to use the expected value definition:

[itex]E[Y]=\int_{-\infty}^\infty uf_Y(u)du[/itex]

then I would have to figure out the pdf of Y.

I'm having trouble remembering how to get the pdf of Y, is there a more explicit way to derive the expected value?

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# Exponential of Gaussian Distribution

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