Which of the following is true about the beta distribution's interval in this context?

• A. It is defined on the entire real line.
• B. It is defined on [0,1].
• C. It is defined on a finite interval between A and B.
• D. It is undefined.

Answer: (C)

The beta distribution has finite support—the density is nonzero only on a bounded interval. In its standard form the interval is [0, 1], and outside that range the density is zero. When a problem uses a specific range [A, B], the beta distribution can be scaled to that interval, so the distribution’s interval becomes a finite segment between A and B. That’s why the statement about being defined on a finite interval between A and B is the best description in this context. It isn’t defined on the entire real line, nor is it undefined—the density is well-defined on that finite interval. Note that [0, 1] is the canonical form, but the context here emphasizes the applied interval [A, B].