Final answer:
The domain of a function or random variable includes all possible values it can take, which can be numerical or categorical. Discrete random variables have specific characteristics, including a countable domain and associated probabilities that sum up to 1. Understanding domains and ranges helps in preventing errors and illogical results in calculations.
Step-by-step explanation:
The question concerns the domain and range of functions and discrete random variables. Specifically:
- The domain of a variable like X, which represents a student's major, includes all possible majors offered at the university.
- The domain of Y, representing the number of classes taken, would be all non-negative integers up to the maximum allowed by the university.
- For Z, the domain is any non-negative amount of money that could be spent on books.
- X, Y, and Z are considered random variables because their values are determined by the outcomes of a specific activity or experiment.
An invalid value such as z = -7 for the amount spent on books highlights the importance of understanding the appropriate domain and range to prevent logical inconsistencies. The essential characteristics of a discrete probability distribution are a finite or countably infinite domain and a probability assigned to each possible outcome that falls between 0 and 1, summing up to 1.