# One over a Normal Distribution

If X is a normal distribution $N(0,\sigma^2)$ is $\frac{1}{X}$ any sort of "official" distribution or something that should just be computed?

In particular I'm looking to find the expectation $E[\frac{1}{X}]$ where X is a Brownian motion.

-
 It has a name (Recinormal Distribution!) and comes up in some applications. – André Nicolas Dec 1 '12 at 7:05 @AndréNicolas, I filled in your rain example comment. So it did not go to waste. Even though it it gone forever. – Will Jagy Dec 1 '12 at 7:17 @AndréNicolas Interesting. Can it have a finite mean and variance? – Dirk Calloway Dec 1 '12 at 8:20 @Dirk Are you reading the answers to your questions? – Did Dec 1 '12 at 11:13 @did I am I was just wondering if there was some exceptional cases involving this Recinormal Distribution – Dirk Calloway Dec 1 '12 at 19:17

As I answered to your previous question, $E[1/X]=\infty$ for a normal distribution.