After some algebra; Var[2_Rand()-1]=1/3
Because the distribution function is even, the mean is zero.
Then using Stdev=sqrt(Var) we get that one standard deviation of this new uniform deviate is 1/¦3.
In order to have a uniform deviate with a unity standard deviation, we must multiply by ¦3.
The new modified uniform deviate (MUD) is then ¦3_(2_Rand()-1) and will have unity variance