Kehl Dániel schrieb: If I'm not missing something, this inner loop is just a waste of time 9999 out of 10000 times because you don't do anything with the generated u and u2. See above. I'm not sure what's the background for this analysis, but it seems to me that in this case you could calculate the theoretical standard deviation for the transformed series quite easily. u2 is a discrete random variable, where maybe something like 40% of the mass is at zero (to get the actual result, if Phi(x) is the cdf of the standard normal, this should be Phi(0.5)-Phi(-0.5), then another 30% or so at plus and minus 1 (Phi(1.5)-Phi(0.5) and Phi(-0.5)-Phi(-1.5)) and so forth. No need to run simulations. I can easily imagine (in fact I find it intuitive in this case) that the theoretical SD of u2 is higher than that of u. HTH, sven