Which statement is correct with respect to empirical probability distributions?

Which statement is correct with respect to empirical probability distributions?

• A. Event categories (bins) are designed so that only the most probable events are included.
• B. The sum of all empirical probabilities in a distribution can be any number.
• C. They provide a mutually exclusive, collectively exhaustive list of outcomes.
• D. Any given event can fall into one or more categories of event (bins).

Answer: (C)

Empirical probability distributions are built by partitioning the possible outcomes into categories that do not overlap and together cover all possibilities. Each observed outcome fits into exactly one category, and every possible outcome has a category, so the set of categories is mutually exclusive and collectively exhaustive. The frequencies in these categories, when converted to probabilities, must sum to 1 because they account for every observation in the dataset. This makes the statement describing the distribution as a mutually exclusive, collectively exhaustive list of outcomes correct. The other ideas don’t fit: partitions aren’t limited to the most probable outcomes, probabilities must sum to 1, and a single event should not fall into multiple categories in a proper empirical distribution.

Empirical probability distributions are built by partitioning the possible outcomes into categories that do not overlap and together cover all possibilities. Each observed outcome fits into exactly one category, and every possible outcome has a category, so the set of categories is mutually exclusive and collectively exhaustive. The frequencies in these categories, when converted to probabilities, must sum to 1 because they account for every observation in the dataset. This makes the statement describing the distribution as a mutually exclusive, collectively exhaustive list of outcomes correct. The other ideas don’t fit: partitions aren’t limited to the most probable outcomes, probabilities must sum to 1, and a single event should not fall into multiple categories in a proper empirical distribution.