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.
Subject:
Mathematics and Statistics, Science and Technology
This is a course on the fundamentals of probability geared towards first- or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in 6.431 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in more depth. There are also a number of additional topics, such as language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; deeper understanding of conditional distributions and expectations.
Modeling, quantification, and analysis of uncertainty. Formulation and solution in sample space. Random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. Interpretations, applications, and lecture demonstrations.
This module defines several key terms related to Probability. The original module by Susan Dean and Dr. Barbara Illowsky in the textbook collection Collaborative Statistics has been modified by Roberta Bloom.
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