In mathematics, specifically in number theory, a binomial number is an integer which can be obtained by evaluating a homogeneous polynomial containing...

theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence...

the negative binomial distribution, also called a Pascal distribution, is a discrete probability distribution that models the number of failures in...

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem...

mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is...

Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients...

Binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories...

monomials. A binomial is a polynomial which is the sum of two monomials. A binomial in a single indeterminate (also known as a univariate binomial) can be...

\alpha } is any complex number, and the power series on the right-hand side is expressed in terms of the (generalized) binomial coefficients ( α k ) =...

binomial regression is a regression analysis technique in which the response (often referred to as Y) has a binomial distribution: it is the number of...

In combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences. It is closely...

In mathematics the nth central binomial coefficient is the particular binomial coefficient ( 2 n n ) = ( 2 n ) ! ( n ! ) 2  for all  n ≥ 0. {\displaystyle...

filters) Binomial series Binomial theorem Binomial transform Binomial type Carlson's theorem Catalan number Fuss–Catalan number Central binomial coefficient...

words, a binomial proportion confidence interval is an interval estimate of a success probability   p   {\displaystyle \ p\ } when only the number of experiments...

In computer science, a binomial heap is a data structure that acts as a priority queue. It is an example of a mergeable heap (also called meldable heap)...

In taxonomy, binomial nomenclature ("two-term naming system"), also called binary nomenclature, is a formal system of naming species of living things by...

The binomial approximation is useful for approximately calculating powers of sums of 1 and a small number x. It states that ( 1 + x ) α ≈ 1 + α x . {\displaystyle...

each of a fixed or known number of Bernoulli trials is either unknown or random. The beta-binomial distribution is the binomial distribution in which the...

In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses...

which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities p n ( x + y ) = ∑ k = 0...

In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials...

A binomial process is a special point process in probability theory. Let P {\displaystyle P} be a probability distribution and n {\displaystyle n} be a...

highest power of a prime number p that divides a given binomial coefficient. In other words, it gives the p-adic valuation of a binomial coefficient. The theorem...

bounds on the number of ways of expressing t as a binomial coefficient" (PDF), INTEGERS: The Electronic Journal of Combinatorial Number Theory, 7: #A53...

mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics...

Abel's binomial theorem, named after Niels Henrik Abel, is a mathematical identity involving sums of binomial coefficients. It states the following: ∑...

seventh square number, 49. 70 is the fourth central binomial coefficient, preceding { 1 , 2 , 6 , 20 } {\displaystyle \{1,2,6,20\}} , as the number of ways to...

In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success"...

OEIS Foundation. Retrieved 2016-05-31. "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia of...

natural number following 125 and preceding 127. As the binomial coefficient ( 9 4 ) {\displaystyle {\tbinom {9}{4}}} , 126 is a central binomial coefficient...