Probability and Statistics in Engineering with Risk Analysis

Engineering decisions must constantly account for real-world uncertainty, variable environmental factors, and system risks. This text-based course provides a clear, structured path to understanding how probability and statistics are applied to solve complex engineering challenges. You will learn to quantify risk, predict system reliability, and make informed decisions using modern statistical frameworks. By working through this course, you will transition from basic mathematical concepts to advanced engineering analysis, gaining the confidence to model random processes and interpret statistical data accurately. You will study fundamental probability theory, explore how uncertainty propagates through physical systems, and learn to apply these concepts to real-world infrastructure and design problems. What you'll learn: - Understand foundational probability concepts, random variables, and probability distributions used in engineering - Analyze system reliability and calculate the propagation of uncertainty through engineering models - Apply Bayesian analysis and risk-based decision theory to evaluate engineering alternatives - Perform parameter estimation and hypothesis testing to validate experimental data - Model time-dependent engineering phenomena using Poisson and Markov processes - Build and interpret simple and multiple linear regression models for engineering datasets The course begins with essential terminology, probability axioms, and foundational distribution types. From there, you will progress to multi-variable systems, statistical inference, regression analysis, and stochastic processes, with each concept illustrated by practical engineering scenarios. This course is designed for engineering students, practicing engineers, and technical professionals who want a solid foundation in probability and statistics. No advanced statistical background is required, though a basic understanding of calculus is helpful to get the most out of the mathematical derivations. Start mastering the tools of engineering risk analysis and statistical modeling today.