for all <math>i</math>. TheseTherefore twothe requirementsset show thatof stochastic vectors havecoincides a geometric interpretation: A stochastic vector is a point onwith the "far face" of a [[Simplex#The_standard_simplex|standard orthogonal [[<math>(n-1)</math>-simplex]]. ThatIt is, a stochasticpoint vectorif uniquely identifies<math>n=1</math>, a pointsegment onif the<math>n=2</math>, facea opposite(filled) oftriangle theif orthogonal<math>n=3</math>, cornera of(filled) the[[tetrahedron]] standard simplex.<refmath>{{citationn=4</math>, etc.
| last1 = Gibilisco | first1 = Paolo
| last2 = Riccomagno | first2 = Eva
| last3 = Rogantin | first3 = Maria Piera
| last4 = Wynn | first4 = Henry P.
| contribution = Algebraic and geometric methods in statistics
| mr = 2642656
| pages = 1–24
| publisher = Cambridge Univ. Press, Cambridge
| title = Algebraic and geometric methods in statistics
| year = 2010}}. See in particular [https://books.google.com/books?id=ijupJxl-4hgC&pg=PA12 p. 12].</ref>
