The presentation in this book of the application of commutative algebra in probability and statistics has proceeded in two basic stages. In Chapters 2, 3 and 4, the emphasis is on the application of algebraic aspects to experimental design. In the present chapter, algebraic constructions are carried out for discrete ﬁnite probability distributions, replacing the design, as a set of discrete points, by the support of a discrete distribution. The algebraic encoding of the basic setting of probability and statistics
in the case of a ﬁnite sample space is carried out in a sequence of steps.