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This paper is concerned with the problems of passivity and passification for a class of uncertain switched systems subject to stochastic disturbance and time-varying delay. The passivity property is adopted to analyze the influence of the external disturbance on such systems to achieve prescribed attenuation levels. Based on average dwell time approach, free-weighting matrix method, and Jensen's integral inequality, delay-dependent sufficient conditions are obtained in terms of linear matrix inequalities, which ensure the uncertain switched stochastic time-delay system to be robustly mean-square exponentially stable and stochastically passive. Then, the switched passive controllers are synthesized by linearization techniques. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.