Final answer:
The domain of a mathematical expression is the set of input values for which the expression is defined. For random variables, it includes all the possible outcomes; for example, a student's major, number of classes, or money spent on books. The domain of money spent (Z) would not include negative values.
Step-by-step explanation:
The domain of a mathematical expression is the set of input values for which the expression is defined. In the context of random variables, the domain consists of all the possible values that the random variable can take. For example:
- If X represents a student's major, the domain could be {English, Mathematics, ...}, including all the majors offered or undeclared.
- If Y represents the number of classes taken in a semester, the domain would likely be a set of non-negative integers, such as {0, 1, 2, ...} up to the maximum number of classes allowed.
- If Z represents the amount of money spent on books, the domain would be all non-negative monetary values starting from zero.
Random variables such as X, Y, and Z are considered random because their exact value can only be determined upon completion of an experiment or survey. As for your question about a value of z = -7, it would not be a possible value for Z if Z represents money spent, as you cannot spend a negative amount of money.
The two essential characteristics of a discrete probability distribution are: that it assigns a probability to each value in the domain of the random variable, and the sum of all those probabilities equals one.