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In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p).
A binomial number is an integer obtained by evaluating a homogeneous polynomial containing two terms, also called a binomial. The form of this binomial is x n ± y n {\displaystyle x^{n}\!\pm y^{n}} , with x > y {\displaystyle x>y} and n > 1 {\displaystyle n>1} .
Binomial (polynomial), a polynomial with two terms; Binomial coefficient, numbers appearing in the expansions of powers of binomials; Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition; Binomial theorem, a theorem about powers of binomials; Binomial type, a property of sequences of polynomials; Binomial series, a ...
The number of successes in the first n trials, which has a binomial distribution B(n, p) The number of failures needed to get r successes, which has a negative binomial distribution NB(r, p) The number of failures needed to get one success, which has a geometric distribution NB(1, p), a special case of the negative binomial distribution; The ...
"Binomial nomenclature" is the correct term for botany, [42] although it is also used by zoologists. [43] Since 1961, [44] "binominal nomenclature" is the technically correct term in zoology. [1] A binomial name is also called a binomen (plural binomina) or binominal name. [2]
The number of different walks of n steps where each step is +1 or −1 is 2 n. For the simple random walk, each of these walks is equally likely. In order for S n to be equal to a number k it is necessary and sufficient that the number of +1 in the walk exceeds those of −1 by k.
Binomial regression is closely connected with binary regression. If the response is a binary variable (two possible outcomes), then these alternatives can be coded as 0 or 1 by considering one of the outcomes as "success" and the other as "failure" and considering these as count data : "success" is 1 success out of 1 trial, while "failure" is 0 ...
The central binomial coefficient () is the number of arrangements where there are an equal number of two types of objects. For example, when n = 2 {\displaystyle n=2} , the binomial coefficient ( 2 ⋅ 2 2 ) {\displaystyle {\binom {2\cdot 2}{2}}} is equal to 6, and there are six arrangements of two copies of A and two copies of B : AABB , ABAB ...