The exact stochastic analysis of most real-time systems is becoming unaffordable in current practice. On one side, the exact calculation of the response time distribution of the tasks is not possible except for simple periodic and independent task sets. On the other side, in practice, tasks introduce complexities like release jitter, blocking in shared resources, stochastic dependencies, etc, which can not be handled by the periodic and independent task set model. This paper introduces the concept of pessimism in the stochastic analysis of real-time systems in the following sense: the exact probability of missing any deadline is always lower than that derived from the pessimistic analysis. Therefore, if real-time constraints are expressed as probabilities of missing deadlines, the pessimistic stochastic analysis provides safe results. Some applications of the pessimism concept are presented. Firstly, the practical problems that arise in the stochastic analysis of periodic and independent task sets are addressed. Secondly, we extend to the stochastic case some well known techniques of the deterministic analysis, such as the blocking in shared resources, and the task priority assignment.