Built-in Mathematica Symbol

GeometricDistribution

GeometricDistribution[p]
represents a geometric distribution with probability parameter p.

The probability for value x in a geometric distribution is for non-negative integers, and is zero otherwise. »

GeometricDistribution[p] is the distribution of the number of failures in a sequence of trials with success probability p before a success occurs.

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

Mean and variance of a geometric distribution:

Probability density function:

Mean and variance of a geometric distribution:

Probability density function:

Generate a set of pseudorandom numbers that are geometrically distributed:

Properties based on higher-order moments:

Second moment of a geometric distribution:

The

quantile of a geometric distribution with

:

The probability of at least 5 failures before 1 success for

:

Plot the cumulative distribution function of a geometric distribution:

The probability of getting any real number except a non-negative integer is zero:

Moments can be obtained from the characteristic function:

:

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

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