Which of the following describes discrete random variables?

Discrete random variables are defined as variables that can take on a countable number of values. This means that the possible outcomes of these variables can be listed out or counted, even if the list is infinite. Common examples of discrete random variables include the number of heads in a series of coin flips, the number of students in a classroom, or the result of rolling a die, where outcomes can be clearly enumerated (e.g., 1, 2, 3, 4, 5, 6).

In contrast, continuous random variables can take on any value within a given range, which makes their outcomes uncountable. Therefore, options that suggest a continuous range of values or an infinite number of values without the specification of countability do not accurately describe discrete random variables. Additionally, asserting that random variables are not measurable does not pertain to the nature of discrete random variables, as they are indeed measurable by their countable outcomes.

Thus, the choice that aligns with the definition of discrete random variables is the one that states they can take on a countable number of values.