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Math Help - Proving expected value of lognormal distribution

  1. #1
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    Proving expected value of lognormal distribution

    How would you prove the expected value of a lognormal (\mu, \sigma) distribution:

    E[X]=e^{\mu+\frac{1}{2}\sigma^2}

    I was thinking integrating \displaystyle\int_{-\infty}^{\infty}xf(x) \ dx but it seems too long.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by acevipa View Post
    How would you prove the expected value of a lognormal (\mu, \sigma) distribution:

    E[X]=e^{\mu+\frac{1}{2}\sigma^2}

    I was thinking integrating \displaystyle\int_{-\infty}^{\infty}xf(x) \ dx but it seems too long.
    It's not as long as you think, so try it. You will not infact need to eveluate an integral as after a bit of manipulation you will have something times the integral of the Gaussian between \pm \infty

    Also the lower limit of integration is 0 not -\infty

    CB
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