binomial


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Related to binomial: Binomial coefficient, binomial distribution, Binomial series

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
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) 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.
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), 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 ?
The result of the binomial test related to the second hypothesis of the research is as below.
The results provide an estimate of the number of funds expected to win as a result of skill using the standard binomial distribution.
An important tool for counting subwords is the notion of binomial coefficient of words, a generalization of the classical binomial coefficient for integers.
Second, we examined the model fit using the conventional statistical approaches, including the binomial model and OLS model.
The formula for the n-th term of the right-circulant determinant sequence with binomial coefficients, denoted by [R.
This finding was analogous to the work of Pollard et al (1977) when fitting the negative binomial distribution to groups of players.
This can be overcome by using a negative binomial model that adds a random term that is assumed to be uncorrelated with the model's covariates.
The proposal also addresses Chile's peculiar binomial system for electing parliamentary representatives, saying it should be modified to be more "proportional.
As indicated earlier, the above process assumes a binomial distribution where the production yield is set equal to the mean of the binomial variable.
Over an infinite number of such trials, each combination is expected to be equally frequent (1/4 each); equivalently, the number of boys (or girls) follows a binomial distribution with n = 2 and p = 0.
Pelletier (1998) used a similar approach, with a negative binomial mean-variance assumption, which is a type of Poisson over-dispersion.