# 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.

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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.