Uniform Distribution Calculator

Compute the PDF, CDF (lower probability), upper probability, mean, and variance of a continuous uniform distribution U(a,b) and visualize them on a chart.

Input

Enter the parameters of a continuous uniform distribution U(a,b) and a value x to compute the density, cumulative probability, mean, and variance.

Value x

The point x at which to evaluate the probability

Lower bound a

The lower bound a of the interval

Upper bound b

The upper bound b of the interval (greater than a)

Result

Lower probability F(3) for U(0, 10)

0.3

Upper probability 1 - F(x)

0.7

Density f(x)

0.1

Mean

Variance

8.33333333

Probability density function (PDF)

Cumulative distribution function (CDF)

How it works

The continuous uniform distribution U(a,b) gives equal probability to every value between a and b.
The probability density is constant inside the interval, f(x) = 1 / (b - a), and 0 outside it.
The cumulative distribution (lower probability) is F(x) = (x - a) / (b - a) inside the interval, 0 when x is below a, and 1 when x is above b.
The upper probability is 1 - F(x).
The mean is (a + b) / 2 and the variance is (b - a) squared divided by 12.
The upper bound b must be greater than the lower bound a.

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