# Average of the numbers given by a linear congruential generator

Show that the average of numbers given by a full cicle of a linear congruential generator with full lenght period is $$\frac{1}{2}-\frac{1}{2m}$$, whith $$m$$ as the module of the generator.

I began by using the definition of a linear congruential generator and the Hull & Dobell theorem, but I got lost in a cycling argument.

• You should define $m$. – Ross Millikan Aug 21 '20 at 23:03
• Yeah, I'm sorry, $m$ is the module. – Davshock Aug 21 '20 at 23:40

• If $m$ is the module, it has $m$ different values, with the first one equals cero, so the average is $(m-1)/2$. – Davshock Aug 21 '20 at 23:48
• I believe you are to divide once more by $m$ so the output is between $0$ and $1$. That gives just what you need. – Ross Millikan Aug 22 '20 at 0:09