For a standard Cauchy distribution f(x)=1/(π(1+x2))f(x) = 1/(\pi(1+x^2))f(x)=1/(π(1+x2)), why does the variance not exist?
The integral for E[X2]E[X^2]E[X2] diverges.
The mean is undefined.
The distribution is not symmetric.
The tails are too thin.