This module contains a review of the basic concepts of probability.
Covers computational and data analysis techniques for environmental engineering applications. First third of subject introduces MATLAB and numerical modeling. Second third emphasizes probabilistic concepts used in data analysis. Final third provides experience with statistical methods for analyzing field and laboratory data. Numerical techniques such as Monte Carlo simulation are used to illustrate the effects of variability and sampling. Concepts are illustrated with environmental examples and data sets. This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environmental Applications (1.017) and Uncertainty in Engineering (1.010), are being jointly offered and taught as a single course.
This module covers the basic ideas of Probability Theory. It reviews the laws of boolean algebra, describes how to compute a priori and conditional probabilities, and uses these properties to obtain Bayes' Rule.
Fundamentals of characterizing and recognizing patterns and features of interest in numerical data. Basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. Decision theory, statistical classification, maximum likelihood and Bayesian estimation, non-parametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research.
This lesson combines conditional probability and combinations to determine the probability of picking a fair coin given that it flipped 4 out of 6 heads. [Probability playlist: Lesson 16 of 29]
This lesson introduces conditional probability. [Probability playlist: Lesson 9 of 29]
This lesson explains conditional probability and touches on Bayes' Theorem. [Probability playlist: Lesson 12 of 29]
This lesson is an introduction to Bayes' Theorem. [Probability playlist: Lesson 13 of 29]
A work in progress, this FlexBook is an introduction to theoretical probability and data organization. Students learn about events, conditions, random variables, and graphs and tables that allow them to manage data.
CK-12 Foundation's Basic Probability and Statistics - A Short Course is an introduction to theoretical probability and data organization. Students learn about events, conditions, random variables, and graphs and tables that allow them to manage data.
This course introduces students to probability and random variable. 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 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.
