  A long-standing open problem in the semantics of programming languages
supporting probabilistic choice is to find a commutative monad for probability
on the category DCPO. In this paper we present three such monads and a general
construction for finding even more. We show how to use these monads to provide
a sound and adequate denotational semantics for the Probabilistic FixPoint
Calculus (PFPC) -- a call-by-value simply-typed lambda calculus with
mixed-variance recursive types, term recursion and probabilistic choice. We
also show that in the special case where we consider continuous dcpo's, then
all three monads coincide with the valuations monad of Jones and we fully
characterise the induced Eilenberg-Moore categories by showing that they are
all isomorphic to the category of continuous Kegelspitzen of Keimel and
Plotkin.
