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We consider the scattering by a one-dimensional random potential and derive the probability distribution of the corresponding Wigner time delay. It is shown that the limiting distribution is the same for two different models and coincides with the one predicted by random matrix theory. It is also shown that the corresponding stochastic process is given by an exponential functional of the potential.doi:10.1088/0305-4470/30/23/005 fatcat:rwia7avkx5ailoo2qupykuw37i