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date: 14 August 2018

Abstract and Keywords

In this chapter the basics of probability theory are introduced, with particular attention to those topics that are most important for applications in philosophy. The formalism is described in two passes. The first presents finite probability, which suffices for most philosophical discussions of probability. The second presents measure theory, which is needed for applications involving infinities or limits. Key concepts such as conditional probability, probabilistic independence, random variables, and expectation are defined. In addition, several important theorems, including Bayes’ theorem, the weak and strong laws of large numbers, and the central limit theorem are defined. Along the way, several familiar puzzles or paradoxes involving probability are discussed.

Keywords: probability, distributions, expectation, conditional probability, Kolmogorov’s axioms, probabilistic independence, probability paradox, random variable, limit theorem

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