In some practical situations, experts cannot gauge the probabilities p1,...,pn of different events; instead, they can estimate a_(ij) the ratios a_(ij) = P_i/p_j of these probabilities. Sometimes, we know the upper bounds Δ_(ij) on the accuracy of these estimates; in this case, we know that each actual ratio a_(ij) belongs to the interval [a_(ij),a_(ij)], where a_(ij) = a_(ij)－ Δ_(ij) and a_(ij) = a_(ij) + Δ_(ij). Based on these intervals, we would like to find the interval estimates [(p)_i,(P)_j] for the probabilities p_i.
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