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We analyze the ability of a stochastic coverage algorithm to achieve both accurate threat-based coverage and effective information capture. When mobile sensors are used to cover the region over time, the goal of threat-based coverage is to allocate the sensors' coverage time between the subregions in proportion to their threat levels. We show that, in contrast to prior results on mobile coverage for maximizing simple event capture, limiting mobility by strategically pausing the sensor is important for threat-based coverage of physical world monitoring. Besides being energy efficient, pausing has two desirable effects. First, it can improve the accuracy of the threat-based coverage, in particular, the accuracy increases monotonically with a pause time parameter, and a large enough parameter will ensure exact matching of the sensor's coverage profile with the region's threat profile. Second, diverse natural phenomena require a non-negligible sensing time to overcome statistical uncertainties posed by the random nature of the phenomena. Suitable pausing allows a subregion to be observed long enough for reliable results.