A poisson distribution displays discrete random variables, according to the University of Glasgow. Examples of discrete random variables include the numbers of cars that pass through an intersection in a given period of time. A discrete random variable is a representation of a countable number of separate values; this variable is always a finite number. Discrete random variables follow a poisson distribution.
Discrete random variables are essentially counts; they are distinguished from continuous random variables because they are not measurements with expected growth. A discrete random variable is the number of the quantity in question, in a given area, within a given time. To provide an analogy in the difference between a discrete random variable and a continuous random variable, the discrete random variable is a snapshot of time, while a continuous random variable is streaming footage.
To further illustrate the property of discrete random variables, in a real life example, consider the number of phone calls received at a call center in an elapsed period of time. A poisson distribution requires that an event or variable is independent of previous occurrences. The phone calls received at one hour are independent of the phone calls received in another hour. The phone calls are counted within certain hours, and these serve as the data of the discrete random variables. Variables that follow a poisson distribution are usually counted.