Continuous Probability Distributions

Continuous probability distributions cover random variables measured on a continuum (time, length, error, concentration) and the probability tools used to model them. This chapter focuses on core distributions such as the normal (Gaussian), uniform, exponential, gamma, beta, lognormal, Weibull, and the common inference distributions (t, chi-square, and F), along with the key ideas behind probability density functions (PDF) and cumulative distribution functions (CDF).

The calculators and explanations support practical tasks like finding probabilities over intervals, left-tail/right-tail areas, z-scores, percentiles (quantiles), critical values, and p-values, with step-by-step work that helps learners see how each result is produced. It’s designed to be accessible for beginners learning continuous probability while still being useful for intermediate and advanced users working with distribution properties, parameter changes, and real data-driven modeling.

Students can verify homework instantly, teachers can generate clear examples and checks for lessons, and self-learners can build intuition for how continuous models behave in applications like reliability, waiting times, measurement error, and hypothesis testing. Use this page to compute accurate results quickly, compare distributions, and strengthen probability and statistics skills with dependable calculations and clear reasoning.