Binomial Distribution. The binomial distribution (the term first used by Yule, 1911) is defined as:

f(x) = [n!/(x!*(n-x)!)] * px * qn-x
for x = 0, 1, 2, ..., n

where
p     is the probability of success at each trial
q     is equal to 1-p
n     is the number of independent trials