Final answer:
The domain of an expression is the set of all possible inputs. For random variables X, Y, and Z, the domain can include categories of majors, non-negative integers for classes taken, and all non-negative real numbers for money spent on books, respectively. The correct option is A.
Step-by-step explanation:
To find the domain of an expression, we are looking for a set of all possible inputs that can be put into a function or a random variable. In the context of probability and random variables:
- If X represents a student's major, then the domain of X includes all academic majors offered by a university, plus undeclared—essentially, it is a set of categories.
- For Y, which represents the number of classes taken in the previous semester, the domain is the set of all non-negative integers that a student could possibly take.
- The domain of Z, representing the amount of money spent on books in the previous semester, is the set of all real numbers greater than or equal to zero, as one cannot spend a negative amount on books.
X, Y, and Z are considered random variables because they can take on any value within their domains, and these values are only known after data collection or an experiment is conducted.
Regarding the question about z = -7, since it is a negative value and one cannot spend a negative amount on books, this would not be a possible value for Z.
The two essential characteristics of a discrete probability distribution are that the sum of all probabilities must equal one, and each individual probability must be between zero and one, inclusive.