# binomial

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## binomial

(bī'nō`mēəl), polynomial expression (see polynomialpolynomial,
mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a1x
) containing two terms, for example, x+y. The binomial theorem, or binomial formula, gives the expansion of the nth power of a binomial (x+y) for n=1, 2, 3, … , as follows:

where the ellipsis (…) indicates a continuation of terms following the same pattern. For example, using the formula and reducing fractions, one obtains (x+y)5=x5+5x4y+10x3y2+10x2y3+5xy4+y5. The coefficients 1, n, n (n−1)/1·2, etc., of x and y may also be found from an array known as Pascal's triangle (for Blaise PascalPascal, Blaise
, 1623–62, French scientist and religious philosopher. Studying under the direction of his father, a civil servant, Pascal showed great precocity, especially in mathematics and science.
), formed by adding adjacent numbers to find the number below them as follows:

## binomial

[bī′nō·mē·əl]
(mathematics)
A polynomial with only two terms.

## binomial

1. a mathematical expression consisting of two terms, such as 3x + 2y
2. a two-part taxonomic name for an animal or plant
3. referring to two names or terms
References in periodicals archive ?
We can go beyond the first two moments of the company's exposure and compute the entire distribution by recognizing that a sum of independent Bernoulli trials is Binomially distributed.
For a more formal test of when regional means deviated significantly from the overall mean, we used the [chi square] test, because the data were binomially distributed.
7] If a randomly selected group member contributes with probability [theta], the number of contributors among the other n group members is binomially (n, [theta]) distributed.
In this game the behavior of "others" is replaced by a truly binomially (n, [theta]) distributed variable, such that any possible strategic considerations are eliminated.
5) and binomially exponentially stabilizing, which, loosely speaking, means that (1.
Bycatch data in the sea scallop dredge fishery violate the underlying assumptions of the ratio method (Cochran, 1977), largely because sea turtle bycatch is binomially distributed with a nonconstant variance.
to the case where losses of the pool are binomially distributed.

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