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Performance, dependability and quality of service (QoS) are prime aspects of the UML modeling domain. To capture these aspects effectively in a modeling language requires easy-to-use support for the specification and analysis of randomly varying behaviors. This paper introduces an extension of UML statecharts with randomly varying durations, by enriching a specific syntactic construct: The after operator is equipped with (discrete or continuous) probability distributions, determining the duration of the delay caused by this operator. The semantics of this extension is given in terms of a variant of stochastic automata. It is shown how existing model-checking tools can be used to calculate model-inherent QoS characteristics automatically. We study a UML model of an automatic teller machine scenario using this approach.