mean | n p standard deviation | sqrt(n (1 - p) p) variance | n (1 - p) p skewness | (1 - 2 p)/sqrt(n (1 - p) p) kurtosis | (1 - 6 (1 - p) p)/(n (1 - p) p) + 3

P (X = x) = piecewise | p^x binomial(n, x) (1 - p)^(n - x) | 0<=x<=n 0 | (otherwise)

P (X<=x) = piecewise | I_(1 - p)(n - floor(x), floor(x) + 1) | 0<=x=n