Civil Engineering
Overview of statistics in engineering, data collection methods, observational studies versus experiments, and sampling techniques.
Overview of statistics in engineering, data collection methods, and sampling techniques.
Measures of central tendency, dispersion, position, skewness, and kurtosis, including grouped data.
Measures of central tendency and dispersion, including mean, variance, and standard deviation.
Basic probability theory, sample spaces, events, counting rules, and probability rules.
Core concepts of probability: sample spaces, events, axioms, and counting rules.
Understanding how probabilities change when new information is available, including Bayes' Theorem and Independence.
Understanding conditional probability, independent events, and Bayes' Theorem.
Expected value, Binomial, Poisson, Negative Binomial, Geometric, and Hypergeometric distributions.
Analysis of discrete random variables including Binomial, Poisson, and Geometric distributions.
Probability density functions, Normal, Uniform, Exponential, Gamma, Weibull, and Lognormal distributions.
Study of continuous distributions such as Normal, Exponential, Gamma, and Weibull.
Joint probability mass/density functions, marginal and conditional distributions, covariance, and correlation.
Joint, marginal, and conditional distributions, covariance, and correlation.
How sample statistics behave, the Central Limit Theorem, t-distribution, Chi-square, and F-distribution.
The Central Limit Theorem and sampling distributions of the mean.
Point estimation, confidence intervals for means, proportions, and variances, and prediction/tolerance intervals.
Point estimation and confidence intervals for means, proportions, and variances.
Null and alternative hypotheses, Type I/II errors, P-values, and tests for means, proportions, variances, and Goodness-of-Fit.
Hypothesis testing framework, Type I and Type II errors, p-values, and testing means.
Simple and multiple linear regression, correlation coefficients, least squares method, and residual analysis.
Simple linear regression, least squares method, and correlation analysis.
One-way ANOVA, Randomized Complete Block Design (RCBD), and post-hoc tests for comparing multiple means.
Understanding the analysis of variance, comparing multiple means, and the F-test.
Control charts for variables and attributes, process capability indices, and natural tolerance limits.
Principles of statistical quality control, control charts for variables and attributes, and process capability.