Final answer:
The definition of the domain and range relates to all possible inputs and outputs for a function, with each input paired with exactly one output. For a relation to be a function, it must meet these criteria, and for discrete probability distributions, the probabilities must sum to 1 and be within the range 0 to 1 for each outcome.
Step-by-step explanation:
The domain and range of a function are sets of values that the independent variable (domain) and dependent variable (range) can take. When determining whether something is a function, one of the key factors is that each input should have exactly one output. In other words, a function has a domain that contains all possible inputs and a corresponding range of outputs where each input has a single output.
In the context of the student's question, we would look at the given sets for the domain and range to confirm whether the sets could represent a function. Without additional information about the relationship between the domain and range, we cannot definitively conclude whether the described relationships are functions. However, based solely on the given domains and ranges, we cannot rule out that they could represent functions, as long as the mapping is such that each domain value maps to exactly one range value.
For discrete random variables, their domain is a list of values that the variable can take, and for continuous random variables, the domain is a range of values. The two essential characteristics of a discrete probability distribution are that the probabilities must sum to 1.0 and that the probabilities of each individual outcome must be between 0 and 1, inclusive.