 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/27l/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The characteristic function of

S_{n} / n

Φ (ξ / n)^{n} = e^{- n ∣ ξ ∣/ n} = e^{- ∣ ξ ∣} .

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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