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This brief is concerned with the analysis problem of global exponential stability in the mean square sense for a class of linear discrete-time recurrent neural networks (DRNNs) with stochastic delay. Different from the prior research works, the effects of both variation range and probability distribution of the time delay are involved in the proposed method. First, a modeling method is proposed by translating the probability distribution of the time delay into parameter matrices of the transformed DRNN model, where the delay is characterized by a stochastic binary distributed variable. Based on the new method, the global exponential stability in the mean square sense for the DRNNs with stochastic delay is investigated by using the Lyapunov-Krasovskii functional and exploiting some new analysis techniques. A numerical example is provided to show the effectiveness and the applicability of the proposed method.