  A sufficient statistic is a deterministic function that captures an essential
property of a probabilistic function (channel, kernel). Being a sufficient
statistic can be expressed nicely in terms of string diagrams, as Tobias Fritz
showed recently, in adjoint form. This reformulation highlights the role of
split idempotents, in the Fisher-Neyman factorisation theorem. Examples of a
sufficient statistic occur in the literature, but mostly in continuous
probability. This paper demonstrates that there are also several fundamental
examples of a sufficient statistic in discrete probability. They emerge after
some combinatorial groundwork that reveals the relevant dagger split
idempotents and shows that a sufficient statistic is a deterministic dagger
epi.
