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Does a subset with small cardinality represent the whole set?

Assume that we have heavy-tailed distribution $F(x)$ such that \begin{align} F(x)=\mathbb{P}[X\geq x]=x^{-0.5}. \end{align} Then, we produce $N$ independent samples $X_1,X_2,\ldots,X_N$ from this ...
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