  We explore the range of probabilistic behaviours that can be engineered with
Chemical Reaction Networks (CRNs). We show that at steady state CRNs are able
to "program" any distribution with finite support in $\mathbb{N}^m$, with $m
\geq 1$. Moreover, any distribution with countable infinite support can be
approximated with arbitrarily small error under the $L^1$ norm. We also give
optimized schemes for special distributions, including the uniform
distribution. Finally, we formulate a calculus to compute on distributions that
is complete for finite support distributions, and can be compiled to a
restricted class of CRNs that at steady state realize those distributions.
