Monte Carlo Simulation in Business Risk Analysis and Modeling Practice Exam

Modeling a proportion requires a distribution whose values naturally fall between 0 and 1. The Beta distribution fits this need because its support is the interval (0, 1) and it offers two shape parameters that let you shape the density to match how the proportion is likely to behave. The mean is α/(α+β) and the variance depends on α and β, so you can describe symmetric, right-skewed, or left-skewed proportions and adjust how tightly the values cluster around the mean.

Other distributions don’t fit as well. The Normal can take values outside the 0–1 range unless you impose truncation, which can distort the properties you want to preserve. The Uniform assumes every value in [0,1] is equally likely, which is rarely realistic for proportions. The Exponential is defined on the positive real line and is not bounded above, so it cannot represent a proportion between 0 and 1.

In short, the Beta distribution is the most natural and flexible choice for bounded proportions.