In the context of basic probability, does a $probability$ distribution function always have to be defined by a mathematical formula with parameters?

• A. Yes, every $probability$ distribution function must be defined by a mathematical formula with at least one parameter.
• B. A $probability$ distribution function cannot be defined without using calculus.
• C. Only continuous $probability$ distributions require a mathematical formula with parameters; discrete distributions do not.
• D. No, a $probability$ distribution function can be defined by a table or a rule, not necessarily a mathematical formula with parameters.

Answer: (D)

Verified step by step guidance

1. Understand that a probability distribution function (PDF) describes how probabilities are assigned to outcomes of a random variable.
2. Recognize that PDFs can be defined in different ways depending on whether the variable is discrete or continuous.
3. For discrete random variables, the probability distribution can be given by a table or a list of probabilities for each possible outcome, without needing a formula with parameters.
4. For continuous random variables, the PDF is often expressed as a mathematical formula involving parameters, but this is not a strict requirement for all probability distributions.
5. Conclude that a probability distribution function does not always have to be defined by a mathematical formula with parameters; it can also be defined by a rule or a table.