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Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 27L / b / Solution

The characteristic function of

S_{n} / n

is

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.

Solved by gpt-5.6-sol high.

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