# The limits of central limit theorem – part 2

In the previous part we made look through the distribution of sample means for three distributions: Uniform, Cauchy, and Petersburg distribution. The Cauchy and Petersburg distributions do not fulfill the Central Limit Theorem since they have infinite variance (and infinite expected value in “Petersburg” case). Now we will have a look at the numerical results for standard deviation of sample means. As in previous part, we use Uniform distribution only as a reference since it fulfills CLT and we use the same pseud-random number generator (Mersenne-Twister).