Let $f$ be some probability density function with undefined central moments. For example, suppose $f$ is a Cauchy distribution.
Say I draw two samples of size $N=100$ from that distribution. The mean of the first sample could be $1.5$ and the mean of the second sample $-2.3$.
However, since the population distribution $f$ does not have the central moments, calculating the mean values should get me into some trouble? Am I correct?