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Math Help - Gamma variables and transformations

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    Gamma variables and transformations

    If Y ~ N(m, s^2), find the distribution function and then the density function of U = e^Y. Either
    from this or by using the moment generating function of Y, find the mean and variance of U.
    (The random variable U is said to have a lognormal distribution.)
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    Quote Originally Posted by sonitgarg View Post
    If Y ~ N(m, s^2), find the distribution function and then the density function of U = e^Y. Either
    from this or by using the moment generating function of Y, find the mean and variance of U.
    (The random variable U is said to have a lognormal distribution.)
    There are several options. One approach is to find the cdf of U:

    F(u) = \Pr(U < u) = \Pr(e^Y < u) = \Pr(Y < \ln u) = \, ....

    Then recall that the pdf of U is given by f(u) = \frac{dF}{du}. To differentiate you'll need to use the chain rule and the Fundamental Theorem of calculus.

    Of related interest: http://www.mathhelpforum.com/math-he...tribution.html
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