Past exam of the mathematics course of the University of Cambridge / 2018 / ia / Paper 2 / 9F / b

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- Solution b

Solution

For one Bernoulli variable, direct expansion gives

Var F (X_{1}) = p (1 - p) (F (1) - F (0))^{2}

. Applying the law of total variance successively to the coordinates gives the variance tensorization

Var F (X) \leq p (1 - p) i = 1 \sum n E (F (X) - F (X^{i}))^{2} .

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