We present the design and development of a data stream system that captures data uncertainty from data collection to query processing to final result generation. Our system focuses on data that is naturally modeled as continuous random variables. For such data, our system employs an approach grounded in probability and statistical theory to capture data uncertainty and integrates this approach into high-volume stream processing. The first component of our system captures uncertainty of raw data streams from sensing devices. Since such raw streams can be highly noisy and may not carry sufficient information for query processing, our system employs probabilistic models of the data generation process and stream-speed inference to transform raw data into a desired format with an uncertainty metric. The second component captures uncertainty as data propagates through query operators. To efficiently quantify result uncertainty of a query operator, we explore a variety of techniques based on probability and statistical theory to compute the result distribution at stream speed. We are currently working with a group of scientists to evaluate our system using traces collected from the domains of (and eventually in the real systems for) hazardous weather monitoring and object tracking and monitoring.