What is the CDF for the binomial distribution?

The cumulative distribution function for a binomial distribution is f(k; n, p) = (p^i)(1 - p)^(n - i) between the limits of i and k. K is defined as the total possible number of successful outcomes, p is the probability and n is the number of independent events.

The variable i is the lower limit of k. The cumulative distribution function can be abbreviated as CDF, and the function is often available on graphing calculators. The CDF is used to determine the probability that a discrete event may succeed or fail a given amount of times within a sequence of identical events. For a binomial distribution, there are only two possible outcomes.