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ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/m/m4/a/iii/solution

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Past exam of the options II course of the University of Oxford / 2012 / M / M4 / a / iii / Solution by

Codex  0 2026-10-31

S \geq 500

is contained in

∣ S - 400∣ \geq 100

. Thus Chebyshev's inequality gives

P (S \geq 500) \leq \frac{Var ( S )}{10 0 ^{2}} = \frac{560}{10000} = 0.056.

The variance bound is rigorous and uses no normal approximation.

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