# Log-Normal Distribution

The Log-Normal distribution may be used when observations are all positive.

Suppose that the Random Variable X follows a log-normal distribution with parameters μ and σ2, i.e. X~Log-normal(μ,σ2). The Probability Density Function of X is ${f}_{X}\left(x\right)=\frac{1}{x\sigma \sqrt{2\pi }}\mathrm{exp}\left(\frac{-1}{2}{\left(\frac{\mathrm{log}\left(x\right)-\mu }{\sigma }\right)}^{2}\right)$.

The Expected Value of X is [330] and the Variance is [331].