We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real polynomials. Some of the mathematics discussed here would be suitable as extension material for senior pre-university students and first-year undergraduates.