Built-in Mathematica Symbol

DiscreteUniformDistribution

DiscreteUniformDistribution[{i_min, i_max}]
represents a discrete uniform distribution over the integers from i_min to i_max.

The probability for value x in a discrete uniform distribution is constant for integers x such that , and is zero otherwise. »

DiscreteUniformDistribution allows i_min and i_max to be any integers such that i_min<i_max.

Mean and variance of a discrete uniform distribution:

Probability density function:

Mean and variance of a discrete uniform distribution:

Probability density function:

Generate a set of pseudorandom numbers that have the discrete uniform distribution:

Properties based on higher-order moments:

Second moment of a discrete uniform distribution:

The

quantile of a discrete uniform distribution:

Plot the cumulative distribution function of a discrete uniform distribution:

The density functions of discrete uniform random variables are not highly concentrated about their means:

The probability of getting any real number except an integer between min and max is zero:

Moments can be obtained from the characteristic function:

DiscreteUniformDistribution is not defined when min or max is not an integer:

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