What is the definition of a discrete random variable?

What is the definition of a discrete random variable?

• A. It can take any value within a range
• B. It can be represented by infinite outcomes
• C. All possible outcomes can be listed in a finite set
• D. It is always less than zero

Answer: (C)

A discrete random variable is characterized by a finite or countably infinite number of possible outcomes, which can be listed individually. This means that the values the variable can take can be enumerated, such as the number of heads in a series of coin tosses or the number of students in a classroom. Each value corresponds to a specific probability, making it possible to analyze and work with these outcomes using various statistical methods. The option indicating that all possible outcomes can be listed in a finite set accurately captures the essence of discrete random variables. For example, when rolling a die, the possible outcomes—1, 2, 3, 4, 5, and 6—can be explicitly listed. This contrasts with continuous random variables, which can take on any value within a given interval and cannot be easily enumerated. The other options highlight key characteristics of different types of variables but do not apply to discrete random variables in the way described. For instance, the idea of being represented by infinite outcomes pertains more to continuous variables, while the notion of always being less than zero is not a defining property of discrete random variables either; they can take on values that are zero or higher depending on the context.

A discrete random variable is characterized by a finite or countably infinite number of possible outcomes, which can be listed individually. This means that the values the variable can take can be enumerated, such as the number of heads in a series of coin tosses or the number of students in a classroom. Each value corresponds to a specific probability, making it possible to analyze and work with these outcomes using various statistical methods.

The option indicating that all possible outcomes can be listed in a finite set accurately captures the essence of discrete random variables. For example, when rolling a die, the possible outcomes—1, 2, 3, 4, 5, and 6—can be explicitly listed. This contrasts with continuous random variables, which can take on any value within a given interval and cannot be easily enumerated.

The other options highlight key characteristics of different types of variables but do not apply to discrete random variables in the way described. For instance, the idea of being represented by infinite outcomes pertains more to continuous variables, while the notion of always being less than zero is not a defining property of discrete random variables either; they can take on values that are zero or higher depending on the context.