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This paper provides a stochastic approach to the analysis of real-time systems under preemptive priority-driven scheduling. The main idea is to simplify the execution time distributions via random sampling to decrease complexity. This beneficial effect is counterbalanced by an increase in pessimism. However, the proposed analysis is significantly less pessimistic than the classical worst-case deterministic analysis. In addition, it could be tuned according to the memory and time availability. Thus, the proposed method provides, for the first time, a relation between pessimism and computational resources. The testing results show the effectiveness of the sampling approach in terms of practicality and optimism.