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Let $X$ be a uniform variable on $[0,1]$. Then if $\Phi(x)$ is the cumulative distribution function of the standard normal distribution, $\Phi^{-1}(X)$ will have a standard normal distribution. If $Y$ is log-normal distributed then $\ln(Y)$ has a normal distribution. Equivalently, if $X$ is normally distributed then $e^X$ has a log-normal distribution. So we ...

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