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I am stuck with this problem. I am looking for E(1/(1 + e^Z)) where Z is a normally distributed random variable.

I know that E(e^Z) and E(1/e^Z) follow lognormal and inverse lognormal distibution and the means of these distributions are standard results. Of course, is also easy to find E(e^Z + 1).

However regarding my problem, does anyone have a suggestion of how to proceed? I tried to use the moment generating function but got stuck...

Thanks in advance!

/Hejdun

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# Inverse of shifted lognormal

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