Continuous probability distribution
Continuous Uniform distribution
X ~ Uniform(a, b)
Every value in the interval [a, b] is equally likely. It is the continuous analogue of the discrete uniform and the foundation of computer random-number generation.
Explore it interactivelyKey facts
- Notation
- X ~ Uniform(a, b)
- Type
- continuous
- Parameters
- a, b — lower and upper bounds (a < b)
- Support
- [a, b]
- f(x) = 1 / (b − a), for a ≤ x ≤ b
- Mean
- (a + b) / 2
- Variance
- (b − a)² / 12
When to use it
- A random number in a fixed range
- Rounding error
- Arrival time within a known window