Take the following power law distribution $$ p(x) = \frac{\alpha-1}{x_{\rm{min}}} \left(\frac{x}{x_{\rm{min}}}\right)^{-\alpha} $$ with $\alpha > 3$ so that the mean and the variance of the distribution exist.
Assume I can generate $n$ random variables $x_1$, $x_2$, $\ldots$, $x_n$ from this distribution in such a way that $$ \hat{x} = \frac{1}{n} \sum_{i=1}^n x_i $$ becomes an unbiased estimator of $\mathbb{E}[x]$. My question is: for a given relative error, how many samples do I need in order to estimate $\mathbb{E}[x]$?
For concreteness, if I want to achieve a precision of two decimals in the estimation of $\mathbb{E}[x]$ how many samples do I need?