Probability

Quantifying uncertainty. Probability for engineers: axioms, conditional probability and Bayes' theorem, reliability of series and parallel systems, random variables with expectation and variance, and the key discrete and continuous distributions with engineering applications.

• Probability Fundamentals & Bayes — Probability quantifies uncertainty. Learn experiments, sample spaces and events, the axioms, complements, unions and intersections, conditional probability, independence, the multiplication rule, total probability, Bayes' theorem, and reliability of series and parallel systems.
• Random Variables — Random variables attach numbers to uncertain outcomes. Learn discrete and continuous random variables, PMF, PDF and CDF, expectation, variance and standard deviation, moments, linear transformations, and sums of independent variables.
• Discrete Distributions — Count-based models for engineering data. Learn Bernoulli, binomial, geometric, negative binomial, Poisson and hypergeometric distributions — definitions, parameters, PMF, mean and variance, when to use each, engineering examples, and the Poisson approximation to the binomial.
• Continuous Distributions — Models for measurements and lifetimes. Learn uniform, exponential, normal (Gaussian), gamma, beta, Weibull and lognormal distributions — PDFs, parameters, mean and variance, standardising with z-scores, the exponential and Weibull in reliability, and choosing a distribution.