Topic: Uniform, Beta, and Gamma Laws

Worked Calculations Across Four Distribution Families

Uniform Density and CDF on a Finite Interval

Uniform, Triangular, and Arcsine Beta Special Cases

The Gamma Function and Its Recurrence

The Beta-Gamma Ratio Construction

The Beta Integral and Beta-Gamma Identity

Scaling and Standardization of Gamma Variables

Raw and Central Moments of a Uniform Variable

Moments and Variance of Gamma Distributions

Modes and Boundary Behavior of Beta Densities