In this class, students use data and systems knowledge to build models of complex socio-technical systems for improved system design and decision-making. Students will enhance their model-building skills, through review and extension of functions of random variables, Poisson processes, and Markov processes; move from applied probability to statistics via Chi-squared t and f tests, derived as functions of random variables; and review classical statistics, hypothesis tests, regression, correlation and causation, simple data mining techniques, and Bayesian vs. classical statistics. A class project is required.

Methylmercury contamination within fish populations is an important toxin that affect human, animal, and environmental health, serving as a carcinogen (cancer-causing agent) and endocrine-disruptor (compounds that in some way alter the signaling of the hormone system. The impacts of exceeding safe dietary methylmercury levels were tragically made clear in Ontario, Canada, where a First Nations community in Grassy Narrows are living with the consequences of methylmercury poisoning in the fish supply. The fish were contaminated due to the dumping of mercury in the traditional waterways of the First Nation community. In 2016, there were highly publicized protests in Muskrat Falls, Labrador, Canada, where the Inuit people raised direct concerns about the potential for a proposed Nalcor Energy hydroelectric dam, to increase mercury levels in fish in those waters, which are an integral part of their traditional diet. Despite significant protests, the project was completed in 2019 and 41 km were flooded. This module uses these real-world examples as a jumping-off point for exercises that will guide case-study driven discussion on mathematical, biological and ethical concerns.

Methylmercury contamination within fish populations is an important toxin that affect human, animal, and environmental health, serving as a carcinogen (cancer-causing agent) and endocrine-disruptor (compounds that in some way alter the signaling of the hormone system. The impacts of exceeding safe dietary methylmercury levels were tragically made clear in Ontario, Canada, where a First Nations community in Grassy Narrows are living with the consequences of methylmercury poisoning in the fish supply. The fish were contaminated due to the dumping of mercury in the traditional waterways of the First Nation community. In 2016, there were highly publicized protests in Muskrat Falls, Labrador, Canada, where the Inuit people raised direct concerns about the potential for a proposed Nalcor Energy hydroelectric dam, to increase mercury levels in fish in those waters, which are an integral part of their traditional diet. Despite significant protests, the project was completed in 2019 and 41 km were flooded. This module uses these real-world examples as a jumping-off point for exercises that will guide case-study driven discussion on mathematical, biological and ethical concerns.

CK-12 Advanced Probability and Statistics introduces students to basic topics in statistics and probability but finishes with the rigorous topics an advanced placement course requires. Includes visualizations of data, introduction to probability, discrete probability distribution, normal distribution, planning and conducting a study, sampling distributions, hypothesis testing, regression and correlation, Chi-Square, analysis of variance, and non-parametric statistics.

CK-12 Advanced Probability and Statistics Teacher's Edition provides tips and enrichment activities for teaching CK-12 Advanced Probability and Statistics Student Edition. The solution and assessment guides are available upon request.

This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems.

6.780 covers statistical modeling and the control of semiconductor fabrication processes and plants. Topics covered include: design of experiments, response surface modeling, and process optimization; defect and parametric yield modeling; process/device/circuit yield optimization; monitoring, diagnosis, and feedback control of equipment and processes; and analysis and scheduling of semiconductor manufacturing operations.

This course covers signals, systems and inference in communication, control and signal processing. Topics include input-output and state-space models of linear systems driven by deterministic and random signals; time- and transform-domain representations in discrete and continuous time; and group delay. State feedback and observers. Probabilistic models; stochastic processes, correlation functions, power spectra, spectral factorization. Least-mean square error estimation; Wiener filtering. Hypothesis testing; detection; matched filters.

Students are introduced to the technology of flexible circuits, some applications and the photolithography fabrication process. They are challenged to determine if the fabrication process results in a change in the circuit dimensions since, as circuits get smaller and smaller (nano-circuits), this could become very problematic. The lesson prepares students to conduct the associated activity in which they perform statistical analysis (using Excel® and GeoGebra) to determine if the circuit dimension sizes before and after fabrication are in fact statistically different. A PowerPoint® presentation and post-quiz are provided. This lesson and its associated activity are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.

A general statistics course, which includes understanding data, measures of central tendency, measures of variation, binomial distributions, normal distributions, correlation and regression, probability and sampling distributions, Central Limit Theorem, confidence intervals, estimates of population parameters and hypothesis testing. Interpretation and data analysis are emphasized.

This 10-minute video lesson discusses the hypothesis test for difference of means. [Statistics playlist: Lesson 58 of 85]

This 11-minute video lesson looks at Hypothesis Testing and P-values. [Statistics playlist: Lesson 47 of 85]

This 12-minute video lesson discusses large sample proportion hypothesis testing. [Statistics playlist: Lesson 53 of 85]

This 7-minute video lesson discusses one-tailed and two-tailed tests. [Statistics playlist: Lesson 48 of 85]

This 9-minute video lesson discusses the small sample hypothesis test. [Statistics playlist: Lesson 51 of 85]

This 3-minute video lesson discusses Type I Errors. [Statistics playlist: Lesson 50 of 85]

This 7-minute video lesson compares Z-statistics and T-statistics. [Statistics playlist: Lesson 49 of 85]

This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.

Provides students with the basic tools for analyzing experimental data, properly interpreting statistical reports in the literature, and reasoning under uncertain situations. Topics organized around three key theories: Probability, statistical, and the linear model. Probability theory covers axioms of probability, discrete and continuous probability models, law of large numbers, and the Central Limit Theorem. Statistical theory covers estimation, likelihood theory, Bayesian methods, bootstrap and other Monte Carlo methods, as well as hypothesis testing, confidence intervals, elementary design of experiments principles and goodness-of-fit. The linear model theory covers the simple regression model and the analysis of variance. Places equal emphasis on theory, data analyses, and simulation studies.

This course gives an introduction to probability and statistics, with emphasis on engineering applications. Course topics include events and their probability, the total probability and Bayes’ theorems, discrete and continuous random variables and vectors, uncertainty propagation and conditional analysis. Second-moment representation of uncertainty, random sampling, estimation of distribution parameters (method of moments, maximum likelihood, Bayesian estimation), and simple and multiple linear regression. Concepts illustrated with examples from various areas of engineering and everyday life.