Free Uniform Distribution Calculator
Calculate probability density, cumulative probability, and properties of the continuous uniform distribution on [a, b].
PDF f(x)
0.10000000
PDF f(x) vs Lower Bound (a)
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.
Example Calculation
A bus arrives uniformly between 0 and 10 minutes. What is P(arrival <= 7 min)?
- 01PDF = 1 / (10 - 0) = 0.1
- 02CDF = (7 - 0) / (10 - 0) = 0.7
- 03P(X <= 7) = 70%
- 04Mean = (0 + 10) / 2 = 5
- 05Variance = (10 - 0)^2 / 12 = 100/12 ≈ 8.3333
Frequently Asked Questions
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