A structured outline of the module's topics, covering discrete vs. continuous random variables, probability density functions, and key distributions (uniform, normal, exponential, Weibull, log-normal) to guide learners through the module's scope.
Four worked engineering examples — one each for normal, exponential, Weibull, and log-normal distributions — providing problem statements, solution approaches, and Python and R code with visualizations to show learners how to apply each distribution in practical contexts.
A comprehensive reference page covering PDFs, CDFs, and the key continuous distributions (uniform, normal, exponential, Weibull, log-normal) with definitions, formulas, and supporting lecture links for learners to study core concepts.
A landing page linking learners to the Module 5 PowerPoint slides and YouTube lecture video on continuous probability distributions.
A worked engineering problem focused on semiconductor oxide-layer thickness that demonstrates how to plot and interpret PDFs and CDFs, helping learners understand the practical value of distribution visualizations.
This reading introduces the foundational concepts of continuous probability distributions, explaining how they differ from discrete distributions, defining key ideas such as probability density functions and cumulative distribution functions, and preparing learners to study specific continuous distributions used in engineering statistics.
This reading explains the uniform distribution, covering its probability density function, mean, variance, and the property that probability is spread evenly across a fixed interval, enabling learners to apply it to problems where all outcomes within a range are equally likely.
This reading covers the normal distribution, including its bell-curve shape, parameters (mean and standard deviation), standardisation to the Z-distribution, and use of Z-tables, allowing learners to calculate probabilities for normally distributed engineering and real-world variables.
This reading describes the exponential distribution, including its probability density function, rate parameter, mean, memoryless property, and its use in modelling the time or distance between random events, equipping learners to solve reliability and waiting-time problems.
This reading presents systematic methods for computing and interpreting probabilities from uniform, normal, and exponential distributions, walking learners through worked examples so they can translate a described scenario into a numerical probability using the appropriate technique.
This reading applies all three continuous distributions to realistic engineering and professional scenarios, guiding learners through multi-step problems that require selecting the correct distribution, setting up calculations, and interpreting results in context.
A 45-question quiz bank assessing learners' ability to identify appropriate probability distributions and solve problems involving continuous and discrete distributions across engineering scenarios.
A graded discussion assignment in which students use an AI tool to generate visualizations of the Assignment 5 dataset, then evaluate how providing distribution context affects the quality of the AI's output.
A graded assignment using real-style wind turbine gearbox failure data (100 gearboxes, time between failures) in which students fit and analyze continuous probability distributions to support maintenance scheduling decisions.