Uniform Distribution Calculator

Summary

Calculate mean, variance, standard deviation, PDF, CDF, and interval probability for a continuous uniform distribution U(a, b).

How it works

1. Enter the lower bound a and upper bound b of your uniform distribution (a must be less than b).
2. Optionally enter x1 and x2 to compute P(x1 ≤ X ≤ x2).
3. The calculator computes mean = (a+b)/2, variance = (b-a)²/12, and standard deviation = √variance.
4. PDF = 1/(b-a) — constant across the entire interval.
5. CDF(x) = (x-a)/(b-a) for x in [a, b].
6. P(x1 ≤ X ≤ x2) = (x2-x1)/(b-a) for x1, x2 inside [a, b].
7. A range indicator visualizes the full interval and any sub-interval.

Use cases

• Model scenarios where all outcomes between two values are equally likely.
• Compute the probability that a random variable falls in a specific sub-range.
• Find mean and variance for uniform priors in Bayesian analysis.
• Solve textbook probability problems involving continuous uniform distributions.
• Simulate random number generation bounded within [a, b].
• Analyze waiting times or rounding errors modeled as uniform distributions.

Frequently Asked Questions