Why These Distributions Matter
Three Powerful Continuous Models
The Beta, Weibull, and Pareto distributions complete your toolkit for continuous probability. Each serves a distinct purpose and appears regularly on Exam P.
Where You'll See Them
Beta Distribution
Models proportions, percentages, and probabilities themselves. Test pass rates, market shares, batting averages — any quantity constrained to [0, 1].
Weibull Distribution
The workhorse of reliability engineering. Models equipment failure times with flexible failure rates: increasing (wear-out), decreasing (burn-in), or constant (Exponential).
Pareto Distribution
The heavy-tailed distribution behind the “80/20 rule.” Essential for insurance claim modeling, income distributions, and any situation where extreme values dominate.
Connections to What You Know
• Beta(1,1) = Uniform(0,1) — the simplest Beta is the Uniform!
• Weibull(k=1, λ) = Exponential(1/λ) — the Exponential is a special Weibull
• If X ~ Pareto(α, θ), then ln(1 + X/θ) ~ Exponential(α)