Final answer:
The domain and range of a function are dependent on the context of the function and the nature of its variables. Random variables have domains specific to the measured or observed category and are only determined after the experiment or observation. For a discrete probability distribution, probabilities of individual outcomes range from 0 to 1 and sum to 1.
Step-by-step explanation:
The question asks which statement is true regarding the domain and range of each function. However, there is no specific function provided, and hence we cannot answer it directly. Instead, let's define domain and range in general terms using examples.
The domain of a function is the set of all possible input values (x-values) that the function can accept, while the range is the set of all possible outputs (y-values) that the function can produce. For instance, if X represents a student's major, the domain would consist of the set of all majors offered at the institution. If Y represents the number of classes taken in the previous semester, the domain would include all non-negative integers (assuming one cannot take a negative number of classes). If Z represents the amount of money spent on books in the previous semester, the domain would likely be the set of all non-negative real numbers (as one normally cannot spend a negative amount).
Random variables such as X, Y, and Z have domains based on the context of the experiment or observation. They are random because their values are not definite until we observe or measure them. For Z, a value of -7 is not physically possible as you cannot spend a negative amount of money on books, suggesting that the measurement is in error or the value is incorrectly recorded.
A discrete probability distribution, which explains the probability of occurrence of each value of a discrete random variable, must have two essential characteristics: (1) the probability of each outcome is between 0 and 1, inclusive, and (2) the sum of all probabilities is 1.