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 builtin 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]