Basic Probability Theory
by Robert B. Ash
Publisher: Dover Publications 2008
Number of pages: 352
This introductory text surveys random variables, conditional probability and expectation, characteristic functions, infinite sequences of random variables, Markov chains, and an introduction to statistics. Geared toward advanced undergraduates and graduate students. The text does not require measure theory, but underlying measure-theoretic ideas are sketched.
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by Vladislav Kargin - arXiv
Contents: Non-commutative Probability Spaces; Distributions; Freeness; Asymptotic Freeness of Random Matrices; Asymptotic Freeness of Haar Unitary Matrices; Free Products of Probability Spaces; Law of Addition; Limit Theorems; Multivariate CLT; etc.
by William G. Faris - University of Arizona
From the table of contents: Combinatorics; Probability Axioms; Discrete Random Variables; The Bernoulli Process; Continuous Random Variables; The Poisson Process; The weak law of large numbers; The central limit theorem; Estimation.
by Patrick Roger - BookBoon
The book is intended to be a technical support for students in finance. Topics: Probability spaces and random variables; Moments of a random variable; Usual probability distributions in financial models; Conditional expectations and Limit theorems.
by Gane Samb Lo - arXiv.org
The fundamental aspects of Probability Theory are presented from a pure mathematical view based on Measure Theory. Such an approach places Probability Theory in its natural frame of Functional Analysis and offers a basis towards Statistics Theory.