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Function of gaussian random variable

  1. Apr 25, 2004 #1
    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?
  2. jcsd
  3. Apr 25, 2004 #2

    matt grime

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    Science Advisor
    Homework Helper

    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.
  4. Apr 25, 2004 #3
    Thanks a lot
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