Final answer:
The domain for Mr. Foster's quiz is {0, 1, 2, ..., 10}, and the range depends on the student's actual scores. Random variables like student's major, class count, and money spent on books have specific domains based on their contexts.
Step-by-step explanation:
The domain and range in the context of Mr. Foster's 10-Question Quiz refer to the set of possible scores a student can achieve and the actual scores of the students, respectively. The domain for this quiz would be the set of all possible scores, which, assuming each question is worth one point, would be {0, 1, 2, ..., 10}. The range will depend on the actual scores achieved by the students; for example, if no student scores below a 4 or above a 9, then the range would be {4, 5, 6, 7, 8, 9}.
In the context of random variables X (student's major), Y (the number of classes taken), and Z (the money spent on books), the domains are the list of all majors offered, the set of whole numbers up to the maximum number of allowed classes, and any non-negative amount of money, respectively. These are considered random variables because their values are determined by random processes and are not known until observed. A negative value like z = -7 is not a possible value for Z since you cannot spend negative money on books; this is an example of a domain violation.
Essential characteristics of a discrete probability distribution
- The probabilities must add up to 1.
- Each possible outcome has a probability between 0 and 1.