3.5.3.1.2 Binocdf

Definition:

\[prob = binocdf(k, n, p)\] computes the lower tail, upper tail and point probabilities in given value \(k\), associated with a Binomial distribution using the corresponding parameters in \(n\), \(p\).

Here is lower tailed probability:

\[P(X\le k)=\sum_{i=0}^k P(X=i)=\sum_{i=0}^k {n \choose k}p^i(1-p)^{n-i}\]

Parameters:

k (input, int)

The integer \(k\), number of successes, which defines the required probabilities. \(0\le k \le n\)

n (input, int)

The parameter \(n\), number of trials of a Bernoulli process, of the Binomial distribution.\(n\ge 0\).

p (input, double)

The parameter \(p\), probability of success for each trial, of the Binomial distribution.\(0 < p < 1\).

prob(output, double)

The probability.