Example 1: Uniform distribution

A random variable is uniformly distributed $X\sim U(a,b)$ when $f(x)=1/(b-a)$ for $a\leq x\leq b$ and zero otherwise. In other words, the random variable is equally likely to take any value in the interval $[a,b]$. Standard (pseudo)random number generators on computers and pocket calculators generate random numbers from 0 to 1 that are distributed as $X\sim U(0,1)$.