In this context, what do the parameters A and B of the beta distribution define?

• A. They define the minimum and maximum of the distribution's support.
• B. They define the size of the data set.
• C. They determine the skewness.
• D. They calibrate the convergence criteria.

Answer: (D)

The two parameters shape the beta distribution on the unit interval [0, 1]. They control how the probability mass is arranged: whether the distribution is symmetric (A equals B) or skewed toward 0 or toward 1. If A is larger than B, the mass shifts toward 1; if B is larger than A, it shifts toward 0. The exact mean is A/(A+B) and the spread depends on both parameters. Importantly, the endpoints of the support are fixed at 0 and 1, regardless of A and B. These parameters do not set the size of a data set, nor do they calibrate convergence criteria in a Monte Carlo algorithm.