Declaring function as probability distribution?



Hello,

I've been looking for a way to encode some information to make Maxima make
certain simplifications automatically.

Specifically I need to encode the following two properties of probability
distributions:
(1) integrate(p(x),x,minf,inf) = 1, (when working with distributions from
the continuous domain)
(2) p(x)>=0 for all x

declare(p(x), posfun) is almost good enough, but not quite.
I'm unsure how to tell integrate (and sum) that the sum over all values is
known.