Uncertainty in Engineering: Functions of Random Variables and Vectors

Every engineering decision involves managing risk, variability, and incomplete data. To design resilient infrastructure or predict environmental impacts, you must understand how uncertainty propagates through mathematical models. This text-based course provides a clear, structured pathway to mastering the probability concepts required to analyze uncertainty in civil and environmental engineering systems. You will transition from basic statistical definitions to modeling complex, multi-variable engineering scenarios with confidence. What you will learn: Understand foundational concepts of probability, joint distributions, and correlation in engineering systems; Calculate the propagation of uncertainty through linear and non-linear functions of random variables; Analyze random vectors and covariance matrices to model multi-dimensional engineering data; Apply analytical methods to estimate the probability of failure and system reliability; Practice formulating safety margins and risk profiles for engineering design decisions. The course begins with essential terminology and foundational probability theory before guiding you through analytical techniques for mapping input uncertainties to output performance metrics. This course is designed for undergraduate engineering students and practicing professionals who want to build a strong mathematical foundation in risk analysis, with no advanced prerequisites required. Start reading today to make more informed, data-backed engineering decisions under uncertainty.