In statistics, the binomial distribution is a discrete probability distribution that counts the number of successes in a sequence of n independent Bernoulli trials, with a fixed probability p of occurrence of success between trials.
A Bernoulli experiment is characterized by being dichotomous, that is, only two results are possible. One of these is called "success" and has a probability of occurrence p and the other, "failure", with a probability q = 1 - p. In the binomial distribution, the experiment is repeated n times, independently, and the probability of a certain number of successes is calculated.
To represent that a random variable X follows a binomial distribution of parameters n and p, it is written:
Its probability function is
where
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