This paper considers a logic, based on the modal mu-calculus, for describing properties of probabilistic open distributed systems and develops a model-checking algorithm for determining whether or not states in nite-state probabilistic systems satisfy formulas in the logic. The central contribution of the paper is a semantics that distinguishes between observations, the meaning of a temporal formula, and its measure. The ensuing model-checking problem reduces to the calculation of a (particular) solution to a system of non-linear equations.