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 Curtis T. McMullen - Harvard University
Contents: The Sample Space; Elements of Combinatorial Analysis; Random Walks; Combinations of Events; Conditional Probability; The Binomial and Poisson Distributions; Normal Approximation; Unlimited Sequences of Bernoulli Trials; etc.
by David Nualart - Universitat de Barcelona
From the table of contents: Stochastic Processes (Probability Spaces and Random Variables, Definitions and Examples); Jump Processes (The Poisson Process, Superposition of Poisson Processes); Markov Chains; Martingales; Stochastic Calculus.
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 S. R. S. Varadhan - New York University
These notes are based on a first year graduate course on Probability and Limit theorems given at Courant Institute of Mathematical Sciences. The text covers discrete time processes. A small amount of measure theory is included.