A binomial distribution arises from a sequence of independent Bernoulli trials.
Definition
If the following conditions hold:
then the total number of successes, \(X\), has a binomial distribution with parameters n and \(\pi\).
\[ X \;\; \sim \;\; \BinomDistn(n, \pi) \]In most practical applications, the parameter \(\pi\) is an unknown constant, but occasionally we know its value.
Before using a binomial distribution, we must be able to argue from the context that the above three assumptions hold.