Uniform Distribution Calculator — Formula
## How to Calculate Uniform Distribution Properties
### Formulas
**PDF: f(x) = 1 / (b - a)** for a <= x <= b
**CDF: P(X <= x) = (x - a) / (b - a)**
The continuous uniform distribution assigns equal probability density to all values in the interval [a, b]. The probability of falling in any sub-interval depends only on the sub-interval's length relative to the total range. The mean is the midpoint (a+b)/2.
### Formulas
**PDF: f(x) = 1 / (b - a)** for a <= x <= b
**CDF: P(X <= x) = (x - a) / (b - a)**
The continuous uniform distribution assigns equal probability density to all values in the interval [a, b]. The probability of falling in any sub-interval depends only on the sub-interval's length relative to the total range. The mean is the midpoint (a+b)/2.
Exemplo Resolvido
A bus arrives uniformly between 0 and 10 minutes. What is P(arrival <= 7 min)?
- PDF = 1 / (10 - 0) = 0.1
- CDF = (7 - 0) / (10 - 0) = 0.7
- P(X <= 7) = 70%
- Mean = (0 + 10) / 2 = 5
- Variance = (10 - 0)^2 / 12 = 100/12 ≈ 8.3333