Function of gaussian random variable

[Jply]

I'm having trouble showing the following relation:

E(exp(z)) = exp(E(z^2)/2)

where z is a zero-mean gaussian variable and E() is the avg

anyone can help?

[matt grime]

Expectation. Look up the definition of the expectation of f(z), where z is some random variable, and do the integral it gives you. Although you don't have to actually do the integration as such, just show the two integrals are equal.

[Jply]

Thanks a lot