# Is this density function well-known?

1. Feb 5, 2014

### mnb96

Hello,

in a certain context I had to deal with a random variable $Y=e^X$, where X follows a standard normal distribution, i.e. $X\sim N(0,1)$.
I had to calculate the probability density function of Y, which did not seem to be difficult, and I obtained:
$$f_Y(y)=\frac{e^{-\frac{1}{2} \log^2(y)}}{y\sqrt{2\pi}}$$

The question is: does the above density function happen to be so well-known that it already has a name?

2. Feb 5, 2014

### economicsnerd

People call it the log-normal distribution. [It's a silly name: not the log of normal, but rather taking its logarithm gives you something normal. Either way, that's what it's called.]

Wikipedia has a page with the usual basic facts you'd care about: http://en.wikipedia.org/wiki/Log-normal_distribution