# Uniform Distribution

A probability distribution \(U(a, b)\) having the PDF

The parameters \(a\) and \(b\) are equal to the lower and upper bounds respectively.

If \(a\) is equal to zero and \(b\) is equal to one then it is known as the

\[
u_{a,b}(x) =
\begin{cases}
0\quad & x < a\\
1/(b-a)\quad & a\leqslant x ⩽ b\\
0\quad & x > b
\end{cases}
\]

that governs the probability of random variables whose outcomes are equally likely.The parameters \(a\) and \(b\) are equal to the lower and upper bounds respectively.

If \(a\) is equal to zero and \(b\) is equal to one then it is known as the

*standard*uniform distribution.