Which type of random variable can assume a finite number of values?

A discrete random variable is one that can take on a finite or countably infinite number of values. This means it can only assume specific values within a given set, such as integers or whole numbers. For example, the number of students in a classroom or the results of a dice roll are both discrete random variables, as they can only take on whole number values.

In contrast, a continuous random variable can take on any value within a certain range, meaning it can assume an infinite number of possible values, such as measurements like weight or height. The term "random variable" is more general and encompasses both discrete and continuous types, but does not specifically define the finite nature of the values taken on. An empirical distribution, while related to observed outcomes, does not define the nature of the random variable itself.

Thus, focusing exclusively on the definition and characteristics, the correct identification of a random variable that can assume a finite number of values is a discrete random variable.