What is the Uniform Distribution Calculator?

The Uniform Distribution Calculator computes probabilities and the probability density function (PDF) for a continuous uniform random variable. In a uniform distribution, all outcomes within a given range [a,b][a, b][a,b] are equally likely. This tool allows users to calculate both the PDF and the probability that the variable falls between any two values within the range.

How to Use:

1. Enter Minimum Value (a): The smallest possible value of the uniform distribution.
2. Enter Maximum Value (b): The largest possible value; it must be greater than the minimum b>ab > ab>a.
3. Enter Lower Bound (x₁) and Upper Bound (x₂): The interval for which you want to find the probability. Ensure a≤x1≤x2≤ba ≤ x₁ ≤ x₂ ≤ ba≤x1​≤x2​≤b.
4. Click “Calculate”: The calculator computes:
   • PDF f(x): f(x)=1b−af(x) = \frac{1}{b – a}f(x)=b−a1​
   • Probability P(x₁ ≤ X ≤ x₂): P=(x2−x1)⋅f(x)P = (x₂ – x₁) \cdot f(x)P=(x2​−x1​)⋅f(x)
5. Review Result: The output shows the PDF value and the probability for the specified interval.