Final answer:
The domain of a function or random variable consists of all the possible values it can take. The domains for 'X' include a list of university majors, for 'Y' include non-negative integers corresponding to classes taken, and for 'Z' include all real numbers from zero upwards representing money spent. Understanding these domains is crucial for data interpretation.
Step-by-step explanation:
The domain of a function or random variable (RV) is the set of all possible values it can take. In this context, the domain refers to the applicable range for our variables or functions, which are X, Y, and Z in this scenario, representing the student's major, number of classes taken, and amount spent on books, respectively.
The domain of X includes a list of all the majors offered at the university; therefore, it can be a set of words instead of numbers, such as {English, Mathematics, ...}. The domain of Y is the set of all non-negative integers representing the number of classes a student might take. The domain of Z includes any real number from zero upwards, since it represents the amount of money which could be spent.
Essential Characteristics of a Discrete Probability Distribution
The two essential characteristics of a discrete probability distribution include:
- The sum of the probabilities of all possible outcomes is equal to one.
- The probability of each individual outcome is between zero and one, inclusive.
Understanding the domain of these variables and their respective probability distributions is fundamental in interpreting data and making predictions based on statistical models.