Final answer:
The domain of a relation is the set of all x-values that can be input into the function. In given examples, domains of variables X, Y, and Z are determined based on the nature of each variable, which are random variables because their values are not predetermined. The correct answer is option A.
Step-by-step explanation:
The domain of a relation is the set of all possible x-values that can be input into the function or relation. For example:
- If X is a student's major, then the domain of X is the list of all the majors offered at the university.
- If Y represents the number of classes taken in the previous semester, then the domain of Y is the set of all non-negative integers up to the maximum number of classes a student can take.
- If Z is the amount of money spent on books in the previous semester, then the domain of Z is any amount of money starting from zero upwards, as you cannot spend negative money on books.
In the given examples, X, Y, and Z are considered random variables because they can take on any value within their domain which is not known until after data collection.
Regarding data collection, if z = -7 is found, this would not be a possible value for Z, as you cannot spend a negative amount of money. Lastly, the two essential characteristics of a discrete probability distribution are that the sum of the probabilities must equal one, and that each probability is between zero and one, inclusive.