Uniform Distribution Calculator
Calculate statistics and probabilities for the continuous uniform distribution. Every value in the interval [a, b] is equally likely, making this the simplest continuous probability distribution.
The continuous uniform distribution on [a, b] assigns equal probability density to every point in the interval. It is the "flat" distribution, and its PDF is a horizontal line at height 1/(b-a).
Key formulas: Mean = (a + b) / 2, Variance = (b - a)^2 / 12, PDF f(x) = 1/(b-a) for a <= x <= b, CDF F(x) = (x - a) / (b - a). The CDF is a straight line from 0 to 1, reflecting the equal probability across the interval.
Applications: Uniform distributions model scenarios where all outcomes in a range are equally likely: random number generators, rounding errors, arrival times when nothing is known about the pattern, and as a non-informative prior in Bayesian statistics. It also serves as the basis for the probability integral transform, which converts any continuous distribution to uniform.