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I'm struggling to understand a line of FORTRAN code and was hoping someone on here would be able to help me out. These lines of code are meant to generate a flat distribution - I understand that GRNDM(RDUMMY,1) is using FORTRAN's random number generator creating a vector called RDUMMY with an array with length of 1, so that only one random number is generated giving a flat distribution. However I don't understand the function of the second line RND = (RDUMMY-0.5)*SIGMA+XMEAN, why would this be needed to give a flat distribution?

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You are omitting to mention what GRNDM actually does (and that turns out to be not so obvious to find on the internet): It returns random numbers in the interval $[0,1]$, equally distributed. The formula in the second line then produces random numbers in the interval $[\mu-\frac\sigma 2,\mu+\frac\sigma 2]$.

Neither of these are of course "flat" distributions in the sense of having the same probability over the entire range of numbers. Rather, they are flat only in a certain interval (either $[0,1]$ or $[\mu-\frac\sigma 2,\mu+\frac\sigma 2]$) of the real number line.

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