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In this paper we develop a bivariate discrete modifiedWeibull (BDMW) distribution and derived some of its important properties such as joint survival function, marginal survival function, conditional survival function, joint probability generating function and hazard rate function. The significance of additional parameter in BDMW is tested using generalized likelihood ratio test. Also we construct a finite mixture ofBDMWand established its identifiability condition. Certain properties of the mixture model are derived. The parameters of BDMW are estimated through method of maximum likelihood.