Y = binocdf(X,N,P) computes a binomial cdf at each of the values in X using the corresponding number of trials in N and probability of success for each trial in P. X, N, and P can be vectors, matrices, or multidimensional arrays that are all the same size. A scalar input is expanded to a constant array with the same dimensions of the other inputs. The values in N must all be positive integers, the values in X must lie on the interval [0,N], and the values in P must lie on the interval [0, 1].

The binomial cdf for a given value and a given pair of parameters and is

The result, , is the probability of observing up to successes in independent trials, where the probability of success in any given trial is . The indicator function ensures that only adopts values of .

Examples

If a baseball team plays 162 games in a season and has a 50-50 chance of winning any game, then the probability of that team winning more than 100 games in a season is:

1 - binocdf(100,162,0.5)

The result is 0.001 (i.e., 1-0.999). If a team wins 100 or more games in a season, this result suggests that it is likely that the team's true probability of winning any game is greater than 0.5.