Built-in Mathematica Symbol

BinomialDistribution

BinomialDistribution[n, p]
represents a binomial distribution with n trials and success probability p.

The probability for value x in a binomial distribution is for integers from 0 to n. »

BinomialDistribution can be used with such functions as Mean, CDF and RandomInteger. »

Mean and variance of a binomial distribution:

Probability density function:

Mean and variance of a binomial distribution:

Probability density function:

Generate a set of pseudorandom numbers that have the binomial distribution:

Properties based on higher-order moments:

Second moment of a binomial distribution:

The

quantile of a binomial distribution with

and

:

The probability of getting more than 5100 heads from flipping a fair coin 10,000 times:

Plot the cumulative distribution function of a binomial distribution:

The density functions of binomial random variables are highly concentrated about their means:

The probability of getting negative integers, integers beyond n, or non-integer numbers is zero:

Moments can be obtained from the characteristic function:

BinomialDistribution is not defined when p is not between zero and one:

BinomialDistribution is not defined when n is not a positive integer:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: