(probability theory, statistics) The discrete probability distribution of the number of successes in a sequence of n independent trials, each of which yields success with probability p.

(mathematics) A formula giving the expansion of a binomial such as (a+b) raised to any positive integer power, i.e. (a+b)ⁿ. It's possible to expand the power into a sum of terms of the form axᵇyᶜ where the coefficient of each term is a positive integer. For example:

plural of binomial name

(mathematics) The Maclaurin series expansion of the function f(x) = (1 + x)^α, for arbitrary complex α; the series ∑ₖ₌₀ ᪲𝛼 choose kxᵏ, where 𝛼 choose k=(𝛼(𝛼-1)(𝛼-2)…(𝛼-k+1))/(k!).

plural of binomial distribution

(statistics) A discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.

plural of negative binomial distribution