Given a random variable $x\sim N(\mu,\sigma)$
What is the distribution of its exponential transformation $y = e^x$?
Exponential transformation of a Gaussian random variable
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probability
normal-distribution
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0It is called a [Log-normal](https://en.wikipedia.org/wiki/Log-normal_distribution) RV. – 2017-02-13
1 Answers
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The distribution of $Y=e^X$ for $X\sim \mathcal{N}(\mu,\sigma^2)$ is called Log-normal and denoted as $Y\sim\mathcal{LN}(\mu,\sigma^2)$. See also here.