Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 207 / 2 / b / i / Solution

The expected number of failures isHolding the alternative and test size fixed, constant power is equivalent to fixing $V(n_0,n_1)=C$. The ethical allocation problem is thereforeThe Lagrange multiplier stationary equations determine the ratio; the second-order condition requires the constrained stationary point to be a local minimum.