A continuous uniform distribution assigns equal likelihood across a range of real numbers and zero weight outside it. The standard form spans 0.0 to 1.0; other forms use any minimum and maximum. section 15.2 section 15.6
Its probability density function is 1.0 between the bounds and 0.0 elsewhere in the implementation. Unlike a discrete distribution, its support cannot be enumerated, so the abstraction uses weighted doubles and sampling. section 15.2
Checking uniformity with a histogram
Take 100,000 samples, assign values between the histogram bounds to 40 columns, and render vertical bars. A roughly level plot provides an observable check that samples spread across the interval, while random variation explains small deviations.
The continuous form complements the discrete uniform distribution: Random.Next(max) selects equally weighted integers from 0 through max - 1, whereas the continuous form samples real-valued intervals. section 12.3 section 12.2
