binomial
A two-term polynomial.
A binomial is a type of probability distribution that is used to model the outcomes of a series of independent Bernoulli trials. A Bernoulli trial is an experiment that has two possible outcomes, typically labeled as success or failure. In a binomial distribution, the probability of success on each trial is denoted by p, and the probability of failure on each trial is denoted by q, where q = 1-p.
The binomial distribution is characterized by two parameters: n, the number of trials, and p, the probability of success on each trial. The probability of getting exactly k successes in n trials is given by the binomial probability function:
P(X = k) = (n choose k) * p^k * q^(n-k)
where (n choose k) is the number of ways to choose k items from n, and is given by the formula:
(n choose k) = n! / (k! * (n-k)!)
The mean or expected value of the binomial distribution is given by:
E(X) = n * p
and the variance of the distribution is given by:
Var(X) = n * p * q
The binomial distribution is a useful tool for modeling a wide range of phenomena, such as the number of heads that come up when flipping a coin or the number of defective items in a production run.
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