binocdf (Statistics Toolbox)

Binomial cumulative distribution function (cdf)

Syntax

```
Y = binocdf(X,N,P)
```

Description

binocdf(X,N,P) computes a binomial cdf at each of the values in X using the corresponding parameters in N and P. Vector or matrix inputs for X, N, and P must all have the same size. A scalar input is expanded to a constant matrix with the same dimensions of the other inputs. The values in N must all be positive integers, and the values in X and P must lie on the interval [0 1].

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

The result, y, is the probability of observing up to x successes in n independent trials, where the probability of success in any given trial is p. The indicator function I_{(0,1, ... ,}_n₎(i) ensures that x only adopts values of 0, 1, ..., n.

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.

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