Understanding a continuous uniform distribution is fundamental in statistics and probability. This free online Uniform Distribution Calculator allows you to quickly determine the Probability Density Function (PDF), Cumulative Distribution Function (CDF), Expected Value (Mean), and Variance for any given lower (a) and upper (b) bounds. Ideal for educational purposes and quick statistical checks.
Formula:
A continuous uniform distribution, denoted U(a, b), describes a scenario where all outcomes within a given range [a, b] are equally likely. The key formulas are:
- Probability Density Function (PDF):
f(x) = 1 / (b - a)fora ≤ x ≤ b, and0otherwise. - Cumulative Distribution Function (CDF):
F(x) = 0forx < aF(x) = (x - a) / (b - a)fora ≤ x < bF(x) = 1forx ≥ b
- Expected Value (Mean):
E(X) = (a + b) / 2 - Variance:
Var(X) = (b - a)2 / 12
Where:
- a = The lower bound of the distribution.
- b = The upper bound of the distribution.
- x = A specific value within the range (used for PDF/CDF calculations).