Uniform Distribution Calculator Formula
Understand the math behind the uniform distribution calculator. Each variable explained with a worked example.
Formulas Used
PDF f(x)
pdf = 1 / (b - a)CDF P(X <= x)
cdf = (x - a) / (b - a)Mean
mean_val = (a + b) / 2Variance
variance_val = pow(b - a, 2) / 12Standard Deviation
std_dev = (b - a) / sqrt(12)Variables
| Variable | Description | Default |
|---|---|---|
a | Lower Bound (a) | 0 |
b | Upper Bound (b) | 10 |
x | Value (x) | 7 |
How It Works
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.
Worked Example
A bus arrives uniformly between 0 and 10 minutes. What is P(arrival <= 7 min)?
a = 0b = 10x = 7
- 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
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Open Uniform Distribution Calculator