Binomial distribution B(n,p) is a distribution of a number of successes in a sequence of n experiments, each of which yields success with probability p. Important limiting cases of this distribution are Poisson distribution and normal distribution.
If X - binomial random variable:
BinomialDistribution and BinomialCDistribution subroutines calculate P(x ≤ k) and P(x > k) with given n, p and k. Subroutines use the above mentioned formula which calculates the cumulative distribution function by using an incomplete beta-function.
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