Probability & Statistics for IE

The language of variability. Descriptive statistics, probability, continuous distributions, sampling and hypothesis tests, and regression — the foundations of forecasting, quality and simulation.

• Descriptive Statistics — Summarise and visualise data before analysing it. Learn mean, median and mode, range, variance and standard deviation, percentiles, quartiles and IQR, outliers, skewness and kurtosis, histograms, box plots, scatter plots and probability plots.
• 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.
• 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.
• Sampling, Confidence & Hypothesis Tests — Draw conclusions about a population from a sample. Learn sampling distributions and the central limit theorem, standard error, confidence intervals (z and t), hypothesis testing, p-values, Type I and II errors, power and sample size, and common tests (t, paired, two-sample, chi-square).
• Correlation & Regression — Relationships between variables. Learn covariance and the correlation coefficient r, simple linear regression by least squares, slope and intercept, residuals and R², prediction vs extrapolation, multiple and non-linear regression, and why correlation is not causation.