Binominalnej

Binominalnej is the feminine gender form of the Polish adjective binominalny (binomial in English). The word is used to describe things relating to a binomial, a pair of terms or elements, and appears in several disciplines, most often in mathematics, statistics, and linguistics.

In mathematics, a binomial is a polynomial with two terms, such as a + b. The binomial theorem expands the nth power of a binomial: (a + b)^n = sum from k = 0 to n of C(n, k) a^{n-k} b^k, where C(n, k) are the binomial (or dwumianowe) coefficients, equal to n!/(k!(n−k)!). These coefficients quantify how many ways terms can appear in each expansion and have wide use in combinatorics and algebra.

In probability, the binomial distribution describes the number of successes in a fixed number of independent Bernoulli trials with the same success probability. Parameters are n (trials) and p (success probability); the mean is np and the variance is np(1−p). This distribution is closely tied to binomial coefficients and the binomial theorem.

In linguistics, a binomial (binominalny) expression refers to a two-member phrase linked by a coordinating conjunction, often with a sense of balance or emphasis, such as “high and low” or “bread and butter.” Such expressions can function as compounds or fixed collocations in a language.

Etymology traces binomial to Latin binominalis, from bi- (two) and nomen (name). The term underlines the two-component structure common to the concept across fields.