# The Binomial Distribution¶

gsl_ran_binomial(p, n)

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,

$p(k) = {n! \over k! (n-k)! } p^k (1-p)^{n-k}$

for $$0 \leq k \leq n$$.

gsl_ran_binomial_pdf(k, p, 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.

gsl_cdf_binomial_P(k, p, n)
gsl_cdf_binomial_Q(k, p, n)

These functions compute the cumulative distribution functions $$P(k), Q(k)$$ for the binomial distribution with parameters p and n.