Final answer:
The domain and range for a sequence representing a student's major (X), classes taken (Y), or money spent on books (Z) correspond to sets of values relevant to the context. These sets could be non-numerical or numerical such as natural numbers or positive real numbers. As random variables, X, Y, and Z take on values based on the outcome of specific situations and form part of a discrete probability distribution with countable outcomes.
Step-by-step explanation:
The question revolves around identifying the domain and range for a conceptual sequence that continues indefinitely. If the sequence were to represent a student's major (X), the domain would be a set of words describing available majors at a university. If Y represents the number of classes taken, its domain would be the set of natural numbers starting from zero. Similarly, if Z signifies the amount of money spent on books, its domain would be the set of all positive real numbers, including zero, since negative amounts are not practical values for money spent.
These variables, X, Y, and Z, are considered random variables because they can take on any value within their respective domains based on the outcome of a particular situation, which is not predetermined. For example, the specific number of books checked out from a university library (X) can only be determined after the fact. Therefore, the possible values of these random variables can be various depending on the circumstances.
In the context of a discrete probability distribution, these variables have particular characteristics. Namely, they must have a countable set of values and associated probabilities that sum up to one. These characteristics ensure that the distribution is properly defined. For instance, when analyzing the distribution of the number of books checked out, the values can be the set of natural numbers with their corresponding probabilities.