Uniform Distribution Calculator
Calculate P(x1 < X < x2) for a uniform distribution on [a, b].
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Enter the lower bound (a) and upper bound (b) of the uniform distribution, then the query interval x1 to x2. The calculator computes the probability that a random value falls between x1 and x2, along with the mean and standard deviation.
About This Calculator
The continuous uniform distribution assigns equal probability to all values in the interval [a, b]. The probability density is 1/(b-a) everywhere in the interval and 0 outside it. It is the simplest continuous distribution and is used in random number generation, simulation, and modeling uncertainty when all outcomes are equally likely.
Frequently Asked Questions
What is the probability density?
For the continuous uniform distribution on [a,b], the PDF is f(x) = 1/(b-a) for a <= x <= b, and 0 otherwise.
What are the mean and variance?
Mean = (a+b)/2. Variance = (b-a)^2/12. Standard deviation = (b-a)/sqrt(12).
Is there a discrete uniform distribution?
Yes. The discrete uniform assigns equal probability 1/n to each of n outcomes, like rolling a fair die (each face has probability 1/6).