It may assume either a finite number of values or an infinite sequence of values1 pointcontinuous random variablediscrete random variablerandom variable

A random variable can be either discrete or continuous.

A discrete random variable is one that may assume either a finite number of values or an infinite sequence of values. For example, the number of heads in 100 coin flips (this could be any number between 0 and 100), or the number of times a bus arrives at a certain bus stop in a day (this could be any non-negative integer).

A continuous random variable, on the other hand, can take on an infinite number of possible values. For example, the exact amount of time it takes for a student to complete a test (this could be any non-negative real number), or the exact height of a person selected at random (this could be any positive real number).

So, if a variable may assume either a finite number of values or an infinite sequence of values, it is a discrete random variable.