Definitions for "Binomial distribution"
the theoretical frequency distribution of events that have two possible outcomes.
A random variable has a binomial distribution (with parameters n and p) if it is the number of "successes" in a fixed number n of independent random trials, all of which have the same probability p of resulting in "success." Under these assumptions, the probability of k successes (and n-k failures) is nck pk(1-p)n-k, where nck is the number of combinations of n objects taken k at a time: nck = n!/(K!(N-k)!). The expected value of a random variable with the binomial distribution is n_p, and the standard error of a random variable with the binomial distribution is (n_p_(1 ] - p))_.
A probability distribution for the number of times that an outcome with constant probability will occur in a succession of repetitions of a statistical experiment.
Keywords:  mgf, frac, kurtosis, entropy, char
\!| kurtosis =\frac{1-6p(1-p)}{np(1-p)}\!| entropy = \frac{1}{2} \ln \left( 2 \pi n e p (1-p) \right) + O \left( \frac{1}{n} \right) | mgf =(1-p + pe^t)^n \!| char =(1-p + pe^{it})^n \!| }}