What describes a discrete random variable?

• A. A variable that can take on any value
• B. A variable that can take on a countable number of values
• C. A variable that must be a whole number
• D. A variable that varies continuously

Answer: (B)

A discrete random variable is characterized by its ability to take on a countable number of values. This means that the possible outcomes can be enumerated or listed, such as whole numbers. For example, the number of students in a classroom or the number of occurrences of an event in a fixed number of trials are discrete random variables, as they can only assume specific, distinct values (like 0, 1, 2, 3, etc.).

In contrast, a variable that can take on any value is described as a continuous variable, which can assume an infinite number of values within a given range, such as height or weight. The idea that a variable must be a whole number is too restrictive; while discrete random variables often take on whole number values, they can also take on other types of countable values, such as fractions in certain contexts. Lastly, a variable that varies continuously does not align with the definition of a discrete random variable, as it would encompass an infinite range of values rather than a countable set.