We present a novel approach, based on probabilistic formal methods, to developing cross-layer resource optimization policies for resource limited distributed systems. One objective of this approach is to enable system designers to analyze designs in order to study design tradeoffs and predict the possible property violations as the system evolves dynamically over time. Specifically, an executable formal specification is developed for each layer under consideration (for example, application, middleware, operating system). The formal specification is then analyzed using statistical model checking and statistical quantitative analysis, to determine the impact of various resource management policies for achieving desired end-to-end QoS properties. We describe how existing statistical approaches have been adapted and improved to provide analyses of given cross-layered optimization policies with quantifiable confidence. The ideas are tested in a multi-mode multi-media case study. Experiments from both theoretical analysis and Monte-Carlo simulation followed by statistical analyses demonstrate the applicability of this approach to the design of resource-limited distributed systems.