Uniform Distribution Probability Calculator
A uniform distribution probability calculator helps determine the likelihood of events occurring within a specific range in continuous probability distributions. It's essential for statistics, quality control, and risk assessment where outcomes are equally likely between defined limits.
Formula
P(x) = (upper limit - lower limit) / (b - a)
Where [a,b] is the interval and lower/upper are the target range.
How to Use
1. Enter interval values (a and b)
2. Input target range (lower and upper limits)
3. Click Calculate
4. View probability result
5. Use Clear to reset fields
Derivation Process
The uniform distribution formula derives from the principle of equal probability density across [a,b]. The probability density function f(x) = 1/(b-a) for a ≤ x ≤ b. Probability between two points is the integral of f(x) over [lower, upper], resulting in (upper - lower)/(b - a).
FAQ 1: What is uniform distribution?
A uniform distribution describes outcomes with equal probability over an interval. In continuous form, all intervals of same length have equal probability. It's characterized by flat probability density function between parameters a and b.
FAQ 2: When to use this calculator?
Use when you need to find the probability of an event occurring between two values in a continuous system with equal likelihood across its range. Common applications include manufacturing tolerances and random number generation analysis.
FAQ 3: Can it handle decimals?
Yes, the calculator accepts decimal values for all inputs. Ensure proper interval ordering (a < b) and limits within the interval for accurate results. The tool automatically validates inputs before calculation.