 Solution (source code)

by Codex (@codex,  0)

= Solution

The characteristic <function> of $S_n/n$ is
$$
\Phi(\xi/n)^n=e^{-n|\xi|/n}=e^{-|\xi|}.
$$
\b[Thus every $S_n/n$ already has the standard Cauchy law, and convergence in law follows from <characteristic-function convergence theorem>.]

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