A Treatise on Probability was printed by John Maynard Keynes while at Cambridge University. The Treatise criticized the classical theory of probability and introduced a "logical-relationist" theory instead. Bertrand Russell, the co-author of Principia Mathematica, described it as "undoubtedly the most important work on probability that has emerged for a very long time," and a "book as a whole is one which it is impossible to praise too highly." The Treatise is primarily philosophical in nature notwithstanding extensive mathematical formulations. The Treatise presented a proposal to probability that was more subject to variation with evidence than the profoundly quantified standard version. Keynes's notion of probability is that it is a rigorously logical relation between proof and hypothesis, a degree of partial association. Keynes's Treatise is the definitive account of the reasonable interpretation of probabilistic logic, a view of probability that has been maintained by such later efforts as Carnap's Logical Foundations of Probability and E.T. Jaynes Probability Theory: The Logic of Science. Keynes saw numerical probabilities as special cases of probability, that did not have to be quantifiable or even comparable.
The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, ...
Featured topics include permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, much more.
Explains probability using genetics, sports, finance, current events and more.
The text includes many computer programs that illustrate the algorithms or the methods of computation for important problems. The book is a beautiful introduction to probability theory at the beginning level.
This witty, nontechnical introduction to probability elucidates such concepts as permutations, independent events, mathematical expectation, the law of averages and more. No advanced math required. 49 drawings.
Subsequent topics include infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book.
This work provides proofs of the essential introductory results and presents the measure theory and mathematical details in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects.
Covering all aspects of probability theory, statistics and data analysis from a Bayesian perspective for graduate students and researchers.
The hallmark features of this text have been retained in this edition, including a superior writing style and excellent exercises and examples covering the wide breadth of coverage of probability topics.
This text is listed on the Course of Reading for SOA Exam P, and for the CAS Exam ST. Probability and Statistics with Applications: A Problem Solving Text is an introductory textbook designed to make the subject accessible to college ...