A probability distribution for which the set of values for the independent variable such that the distribution function is non-zero has cardinality not greater than aleph-null (i.e. the set is countable).
Examples of discrete distributions:
Note: a distribution is only discrete if the underlying population, not any values recorded, conform th the criterion above. (In particular, the distribution of heights of people, for instance, is continuous even if the recorded values are rounded or truncated.)