## Definition of Log-Normal Distribution

The continuous random variable `$X$`

has a Log Normal Distribution if the random variable `$Y=\ln (X)$`

has a normal distribution with mean `$\mu$`

and standard deviation `$\sigma$`

.

The probability density function of `$X$`

is ```
\[
\begin{equation*}
f(x;\mu,\sigma) =\left\{
\begin{array}{ll}
\frac{1}{\sqrt{2\pi}\sigma x}e^{-\frac{1}{2\sigma^2}(\ln x -\mu)^2}, & \hbox{$x\geq 0$;} \\
0, & \hbox{$x < 0$.}
\end{array}
\right.
\end{equation*}
\]
```

`$\mu$`

is location parameter`$\sigma$`

is scale parameter

Log-Normal Probability Calculator | |
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First Parameter ($\mu$) | |

Second parameter ($\sigma$) | |

P(X< A) | |

P(X > B) | |

P(A< X < B) | and |

Outside A and B | and |

Results | |

Mean : | |

Variance : | |

Required Probability : |