# 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.