Final answer:
The domain of X is the list of all majors, the domain of Y is integers from zero to the upper limit of classes, and the domain of Z is any amount of money from zero upwards. X, Y, and Z are random variables because their values can take any value within their domains. The two essential characteristics of a discrete probability distribution are that the sum of all probabilities is equal to 1, and the probability of each outcome is between 0 and 1.
Step-by-step explanation:
The domain of X is the list of all majors offered at the university, including undeclared. The domain of Y is the set of integers from zero to the upper limit of classes allowed by the university. The domain of Z is any amount of money from zero upwards.
X, Y, and Z are random variables because their values can take any value within their respective domains, and their values for any particular case are not known until the survey is completed.
For the case where z = -7, it is not a possible value for Z because the domain of Z starts from zero upwards, and negative values are not included.
The two essential characteristics of a discrete probability distribution are that the sum of all probabilities is equal to 1, and the probability of each outcome is between 0 and 1.