This function returns a random integer from the binomial distribution, the number of successes in n independent trials with probability p. The probability distribution for binomial variates is,
for \(0 \leq k \leq n\).
This function computes the probability \(p(k)\) of obtaining \(k\) from a binomial distribution with parameters p and n, using the formula given above.
These functions compute the cumulative distribution functions \(P(k), Q(k)\) for the binomial distribution with parameters p and n.