Uniform Distribution (Continuous)

The continuous uniform distribution has an outcome space over a continuous range of values, each of which is equally likely to occur. Here is the PDF:

$$f(X = x) =\begin{cases}1/(b - a), &x \in [a, b]\\0, &otherwise\end{cases}$$

A real-world system this distribution can model is a perfect random number generator. Here, a is the lowest value allowed and b is the highest value allowed, meaning that the generator can produce any rational or irrational value between a and b, each with an equal probability.