A discrete distribution describes the probabilistic properties of a random variable that takes on a set of values that are discrete, i.e. separate and distinct from one another – a discrete random variable . Discrete values are separated only by a finite number of units – in flipping a coin five times, the result of 5 heads is separated from the result of 2 heads by two units (3 heads and 4 heads).
A simple example of a discrete distributions is the binomial distribution . The variables that obey this distribution take on a finite number of values.
The term “discrete distribution” does not necessarily mean that the number of possible values is finite. In other words, “discrete” is not synonymous with “finite”. A simple example of a discrete distribution with an infinite number of possible values is the Poisson distribution .
The opposite (or complementary) concept is continuous distribution , where possible values can be separated by an infinite number of other possible values (e.g. height, weight, distance). Some discrete distributions (e.g. income) may take on so many possible values that they are sometimes treated as continuous.