Interpretations of the concept of probability. Basic probability rules; random variables and distribution functions; functions of random variables. Applications to quality control and the reliability assessment of mechanical/electrical components, as well as simple structures and redundant systems. Elements of statistics. Bayesian methods in engineering. Methods for reliability and risk assessment of complex systems, (event-tree and fault-tree analysis, common-cause failures, human reliability models). Uncertainty propagation in complex systems (Monte Carlo methods, Latin Hypercube Sampling). Introduction to Markov models. Examples and applications from nuclear and chemical-process plants, waste repositories, and mechanical systems. Open to qualified undergraduates.

Explain how a density function is used to find probabilities involving continuous random variables.

This page of Statistical Java describes 11 different probability distributions including the Binomial, Poisson, Negative Binomial, Geometric, T, Chi-squared, Gamma, Weibull, Log-Normal, Beta, and F. Each distribution has its own applet.

Learning Objective: Apply probability rules in order to find the likelihood of an event.

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

" This course develops logical, empirically based arguments using statistical techniques and analytic methods. Elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation are covered. Emphasis is on the use and limitations of analytical techniques in planning practice."

A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Dawson (1995) presented a data set giving a population at risk and fatalities for an “unusual episode” (the sinking of the ocean liner Titanic) and discussed the use of the data set in a first statistics course as an elementary exercise in statistical thinking, the goal being to deduce the origin of the data. Simonoff (1997) discussed the use of this data set in a second statistics course to illustrate logistic regression. Moore (2000) used an abbreviated form of the data set in a chapter exercise on the chi-square test. This article describes an activity that illustrates contingency table (two-way table) analysis. Students use contingency tables to analyze the “unusual episode” data (from Dawson 1995) and attempt to use their analysis to deduce the origin of the data. The activity is appropriate for use in an introductory college statistics course or in a high school AP statistics course.

Students explore the definition and interpretations of the probability of an event by investigating the long run proportion of times a sum of 8 is obtained when two balanced dice are rolled repeatedly. Making use of hand calculations, computer simulations, and descriptive techniques, students encounter the laws of large numbers in a familiar setting. By working through the exercises, students will gain a deeper understanding of the qualitative and quantitative relationships between theoretical probability and long run relative frequency. Particularly, students investigate the proximity of the relative frequency of an event to its probability and conclude, from data, that the dispersion of the relative frequency diminishes on the order .

This activity provides students with 24 histograms representing distributions with differing shapes and characteristics. By sorting the histograms into piles that seem to go together, and by describing those piles, students develop awareness of the different versions of particular shapes (e.g., different types of skewed distributions, or different types of normal distributions), that not all histograms are easy to classify, that there is a difference between models (normal, uniform) and characteristics (skewness, symmetry, etc.).

This activity leads students to appreciate the usefulness of simulations for approximating probabilities. It also provides them with experience calculating probabilities based on geometric arguments and using the bivariate normal distribution. We have used it in courses in probability and mathematical statistics, as well as in an introductory statistics course at the post-calculus level.

In these activities designed to introduce sampling distributions and the Central Limit Theorem, students generate several small samples and note patterns in the distributions of the means and proportions that they themselves calculate from these samples.

An important objective in hiring is to ensure diversity in the workforce. The race or gender of individuals hired by an organization should reflect the race or gender of the applicant pool. If certain groups are under-represented or over-represented among the employees, then there may be a case for discrimination in hiring. On the other hand, there may be a number of random factors unrelated to discrimination, such as the timing of the interview or competition from other employers, that might cause one group to be over-represented or under-represented. In this exercise, we ask students to investigate the role of randomness in hiring, and to consider how this might be used to help substantiate or refute charges of discrimination.

This course is an introduction to statistical data analysis. Topics are chosen from applied probability, sampling, estimation, hypothesis testing, linear regression, analysis of variance, categorical data analysis, and nonparametric statistics.

Introductory statistics course developed through the Ohio Department of Higher Education OER Innovation Grant. The course is part of the Ohio Transfer Module and is also named TMM010. For more information about credit transfer between Ohio colleges and universities please visit: www.ohiohighered.org/transfer.Team LeadKameswarrao Casukhela                     Ohio State University – LimaContent ContributorsEmily Dennett                                       Central Ohio Technical CollegeSara Rollo                                            North Central State CollegeNicholas Shay                                      Central Ohio Technical CollegeChan Siriphokha                                   Clark State Community CollegeLibrarianJoy Gao                                                Ohio Wesleyan UniversityReview TeamAlice Taylor                                           University of Rio GrandeJim Cottrill                                             Ohio Dominican University

ProbabilityThe notion of chance or probability of an event plays a crucial role in statistics. In this module we will study this notion and learn different rules that will help us determine the probability of different types of events associated with a process.Learning Objectives:Random experiment, sample space, eventsPermutation and CombinationDefinition of probability of an event and its propertiesDisjoint and independent eventsConditional eventsVenn and Tree DiagramsComplement (Subtraction) ruleAddition ruleMultiplication ruleDivision ruleTwo-Way tablesTotal Probability Rule and Bayes Rule

Estimation and control of dynamic systems. Brief review of probability and random variables. Classical and state-space descriptions of random processes and their propagation through linear systems. Frequency domain design of filters and compensators. The Kalman filter to estimate the states of dynamic systems. Conditions for stability of the filter equations.

This applet allows the user to adjust the degrees of freedom of the T Distribution with a slider or manual input. The applet allows the user to fix the x and or y axes. The user immediately sees how this affects the shape of the graph.

The applet in this section allows you to see how the T distribution is related to the Standard Normal distribution by calculating probabilities. The T distribution is primarily used to make inferences on a Normal mean when the variance is unknown.