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Upgrading from:

Statistics`DiscreteDistributions`

Distributions defined in this package have been added to the built-in Mathematica kernel.
The input syntax for DiscreteUniformDistribution has changed.
Random and RandomArray are replaced by RandomInteger.

Discrete distributions are now part of the built‐in Mathematica kernel:

Version 5.2 << Statistics`DiscreteDistributions`; Mean[BinomialDistribution[n, p]]

DiscreteUniformDistribution is now parameterized by a pair of integer endpoints {min,max}:

Version 5.2 << Statistics`DiscreteDistributions`; Mean[DiscreteUniformDistribution[max]]

DiscreteUniformDistribution allows for integer ranges for which min is not 1:

Random elements for discrete distributions are generated via RandomInteger:

Version 5.2 << Statistics`DiscreteDistributions`; Random[PoissonDistribution[10]]
Version 5.2 << Statistics`DiscreteDistributions`; RandomArray[PoissonDistribution[10], 5]