While working on an assignment for my machine learning class, I rediscovered the fact that if X is a random variable from a Poisson distribution with parameter , then

where denotes a Stirling number of the second kind. (I actually prefer Knuth’s curly bracket notation, but I can’t seem to get it to work on this blog.) In particular, if , then is the nth Bell number , the number of ways of partitioning a set of size n into subsets!

As it turned out, this didn’t help me at all with my assignment, I just thought it was nifty.

## About Brent

Assistant Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.

I think \left\{k \atop b\right\} worked for me to for bracket notation.

I hope that shows up as code…

Aha, thanks!