Uniform Distribution Calculator
Calculate probabilities for continuous uniform distribution with PDF and CDF visualization
Optional: Enter a value to calculate PDF and CDF at that point
Results
Enter values and click Calculate to see the result.
Theory & Formula
Theory
The uniform distribution is a continuous probability distribution where all values in a given interval [a, b] are equally likely. It is characterized by a constant probability density.
Probability Density Function (PDF)
\(f(x) = \begin{cases} \frac{1}{b-a} & \text{for } a \leq x \leq b \\ 0 & \text{otherwise} \end{cases}\)
Cumulative Distribution Function (CDF)
\(F(x) = \begin{cases} 0 & \text{for } x < a \\ \frac{x-a}{b-a} & \text{for } a \leq x \leq b \\ 1 & \text{for } x > b \end{cases}\)
Properties
\(\text{Mean: } \mu = \frac{a + b}{2}\)\(\text{Variance: } \sigma^2 = \frac{(b - a)^2}{12}\)\(\text{Standard Deviation: } \sigma = \frac{b - a}{2\sqrt{3}}\)
Example
A random number generator produces values uniformly between 0 and 10. What is the probability of getting a value less than 7? Answer: F(7) = 0.7 or 70%