Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 207 / 3 / b / i

Table of contents
- Solution i

Solution

Minimizing the expected failures

n_{H} (1 - p_{H}) + n_{L} (1 - p_{L})

at a fixed variance gives the ethically optimal ratio

\frac{n _{H}}{n _{L}} = \frac{p _{H}}{p _{L}} .

It allocates more patients to the dose with the larger response probability.

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