Final answer:
A random variable can be either discrete or continuous. The domain of a random variable is the set of all possible values it can take on. The range of a random variable is the set of all possible values it can output. So, the correct answer is B. Domain.
Step-by-step explanation:
A random variable can be classified as either discrete or continuous.
A discrete random variable takes on countable values, such as the number of books purchased or the number of classes taken.
A continuous random variable takes on uncountable values, such as the amount of money spent on books or the student's GPA.
The domain of a random variable is the set of all possible values it can take on.
For a student's major (X), the domain would include all majors offered at the university.
For the number of classes taken (Y), the domain would be any non-negative integer. And for the amount of money spent on books (Z), the domain would be any non-negative value.
The range of a random variable is the set of all possible values it can output.
The range of X would be the set of all possible majors offered at the university.
The range of Y would be the set of all non-negative integers. And the range of Z would be all non-negative real numbers.
A random variable can be either discrete or continuous, depending on the nature of the values it can take on. X, Y, and Z in the previous examples are random variables because they can take on different values within their respective domains.
A value of -7 for Z (amount of money spent on books) would not be possible, as the domain of Z includes only non-negative values.
A discrete probability distribution has two essential characteristics: each probability is between zero and one, inclusive, and the sum of the probabilities is one.
Thus, the correct answer is B. Domain.