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We investigate the impact of mobile node density on several detection performance measures for stationary target detection by a hybrid sensor network consisting of both static and mobile nodes. Such hybrid sensor networks are becoming attractive with the recent advances in sensor nodes equipped with mobile platforms. However, adding a large number of mobile nodes to a sensor network for continuous coverage improvement might be expensive due to mobile node's higher energy consumptions compared to that with static nodes. Motivated by these, we investigate the trade-off between the density of mobile nodes and the network performance in a hybrid sensor network with respect to several performance measures of interest, when mobile nodes perform random mobility. We derive analytical (exact and/or approximate) formulae for detection probability, detection latency and mean first contact distance, by applying the theory of coverage processes and use them to evaluate the tradeoff between the fraction of mobile nodes and these performance measures. Analytical results presented in this paper give insights on how to select optimal network parameters in designing hybrid sensor networks to achieve desired performance requirements. Validity of the derived analytical results is verified via Monte-Carlo simulations.