We consider distributed state estimation over a resource-limited wireless sensor network. A stochastic sensor activation scheme is introduced to reduce the sensor energy consumption in communications, under which each sensor is activated with a certain probability. When the sensor is activated, it observes the target state and exchanges its estimate of the target state with its neighbors; otherwise, it only receives the estimates from its neighbors. An optimal estimator is designed for each sensor by minimizing its mean-squared estimation error. An upper and a lower bound of the limiting estimation error covariance are obtained. A method of selecting the consensus gain and a lower bound of the activating probability is also provided. (C) 2014 Elsevier Ltd. All rights reserved.