Final answer:
The domain of the function f(x), where 0 ≤ x ≤ 20, is the interval [0, 20]. For random variables, the domain encompasses all possible outcomes which can be numerical or non-numerical values depending on the experiment or nature of the variable.
Step-by-step explanation:
In mathematics, the domain of a function is the set of all possible input values (typically represented by x) for which the function is defined. When considering the function f(x) given in the question, where 0 ≤ x ≤ 20, the domain is the set of all real numbers between and including 0 and 20. This is because the function is described as a horizontal line within this interval, and x is a real number. Therefore, the domain of f(x) is [0, 20].
For random variables, the concept of domain differs. It is the set of all possible outcomes or values that the random variable can assume. The domain can be numerical or non-numerical depending on the context of the experiment or the nature of the variable. Given examples show domains as a set of academic majors, a count of classes, or an amount of money, which illustrate discrete and continuous domains in various contexts.
Understanding random variables is important, as they are fundamental in probability and statistics. Random variables can be discrete, taking specific values within a range or set, or continuous, taking any value within an interval. The value that a random variable takes is not known until the outcome of the experiment is observed.