Let $M(x)$ denote the expected value at level x of the response to a certain experiment. $M(x)$ is assumed to be a monotone function of x but is unknown to the experimenter, and it is desired to find the solution x = θ of the equation M(x) = α, where α is a given constant. We give a method for making successive experiments at levels x₁,x₂,⋯ in such a way that xₙ will tend to θ in probability.
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Robbins et al. (1951) studied this question.