As mentioned previously, the underlying PDF for the generation of random numbers is the uniform distribution, meaning that the probability for finding a number \( x \) in the interval [0,1] is \( p(x)=1 \).

A random number generator should produce numbers which are uniformly distributed in this interval. The table shows the distribution of \( N=10000 \) random numbers generated by the functions in the program library. We note in this table that the number of points in the various intervals \( 0.0-0.1 \), \( 0.1-0.2 \) etc are fairly close to \( 1000 \), with some minor deviations.

Two additional measures are the standard deviation \( \sigma \) and the mean \( \mu=\langle x\rangle \).