Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 208 / 4 / c / iv

Table of contents
- Solution iv

Solution

Applying part i to the convex function

- g

gives

P (W - E W \leq - t) = P ((- W) - E (- W) \geq t) \leq e^{- t^{2} /2} .

This proves probability (iv). Thus both requested tails of the concave function have the claimed bound.

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