Final answer:
The domain of a function is the set of all possible x values for which the function is defined. In the case of student's majors, classes taken, or money spent on books, it refers to all possible values those variables could be, including lists of options or all non-negative numbers. Random variables have uncertain values before observation, and in a discrete probability distribution, the probabilities sum to 1 and are individually between 0 and 1.
Step-by-step explanation:
The domain of a function refers to the set of all possible x values for which the function is defined. Let's go through your questions:
- If X = student's major, then the domain of X is a list of all the majors offered at the university, including an option for undeclared. This is because a student's major can only be one of the predefined options available at the university.
- If Y = the number of classes taken in the previous semester, the domain of Y consists of the non-negative integers that represent the number of classes a student can take, starting from zero up to the university's maximum allowed number of classes.
- If Z = the amount of money spent on books in the previous semester, the domain of Z includes any non-negative amount of money since students cannot spend a negative amount on books.
- X, Y, and Z are considered random variables because their specific values are not known until the measurement is taken.
- After collecting data, if z = -7, this is not a possible value for Z since you cannot spend a negative amount of money on books.
- The two essential characteristics of a discrete probability distribution are that the sum of all probabilities must be 1, and each individual probability must be between 0 and 1, inclusive.