Probabilistic correctness is another important aspect of reliable systems. A soft real-time system, for instance, exhibits probabilistic behaviors from tolerating some degrees of deadline misses. Since probabilistic systems may behave differently from their probabilistic models depending on their current environments, checking the systems at runtime can provide another level of assurance for their probabilistic correctness. Runtime verification is a technique for checking correctness of a system at runtime by observing a system execution and checking it against its property specification. To check probabilistic properties, runtime verification can adopt a statistical technique used in model checking to check probabilistic properties. The statistical technique simulates, samples many execution paths, and estimates probabilities by counting successful samples against all samples. One particular difficulty in using this technique in runtime verification, however, is that runtime ver...