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This letter presents a simple model for determining energy efficient random sleep-awake schedules. Random sleep-awake schedules are more appropriate for sensor networks, where the time of occurrence of an event being monitored, e.g., the detection of an intruder, is unknown a priori, and the coordination among nodes is costly. We model the random sleep-awake schedule as a two state Markov process, and maximize the probability of the transmission of sensed data by a given deadline. Our results indicate that for a given duty cycle, the optimal policy is to have infrequent transitions between sleep and awake modes, if the average number of packets sent is greater than the mean number of slots the node is awake.