A beta distribution in this context is characterized by how many parameters, and which are they?

• A. Three parameters: α, β, and scale.
• B. Four parameters: α, β, minimum (A), and maximum (B).
• C. Two parameters: α and β.
• D. Five parameters: α, β, A, B, and C.

Answer: (D)

The beta distribution is defined by two shape parameters, α and β, which shape the distribution on its standard support. When you want it on a different interval [A, B], you use a linear transformation so the standard Beta(α, β) on [0, 1] is mapped to [A, B]. That introduces the interval endpoints A and B as additional parameters, giving four parameters in total: α, β, A, and B. A five-parameter version adding an extra parameter (C) isn’t part of the standard specification. So the four-parameter set α, β, A, B is the correct characterization.