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Continuous Uniform Distribution — result sheet
Evaluate the density and cumulative probability of a continuous uniform variable on a finite interval, with its mean and variance.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For a < b, f(x) = 1/(b-a) on [a,b] and 0 outside; F(x) = 0 below a, (x-a)/(b-a) inside, and 1 at or above b; mean = (a+b)/2; variance = (b-a)^2/12.
The continuous uniform model assigns equal density across a finite interval. The calculator evaluates one point and reports distribution moments; it does not treat a single point as having positive probability or convert the model into a discrete table.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Lower bound (a) — minimum -1000000000000; maximum 1000000000000
- Upper bound (b) — minimum -1000000000000; maximum 1000000000000
- Evaluation value (x) — Values outside [a, b] have density 0 and a CDF of 0 or 1.; minimum -1000000000000; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Lower bound (a) | 0 |
| Upper bound (b) | 10 |
| Evaluation value (x) | 4 |
f(4) = 0.1; F(4) = 0.4; mean = 5; variance = 8.333333.
Assumptions and limits
- The variable is continuous and has constant density between the finite lower and upper bounds.
- The upper bound is greater than the lower bound by at least 0.000001 in the entered units.
- No data fitting, truncation correction, measurement error, or discrete rounding is modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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