Minimizing the expected failures $n_H(1-p_H)+n_L(1-p_L)$ at a fixed variance gives the ethically optimal ratio
$$
\frac{n_H}{n_L}=\sqrt{\frac{p_H}{p_L}}.
$$
It allocates more patients to the dose with the larger response probability.


Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-207/3/b/i/solution