An Introduction to Probability Theory and Its Applications, Volume 1

A complete guide to the theory and practical applications of probability theory

An Introduction to Probability Theory and Its Applications uniquely blends a comprehensive overview of probability theory with the real-world application of that theory. Beginning with the background and very nature of probability theory, the book then proceeds through sample spaces, combinatorial analysis, fluctuations in coin tossing and random walks, the combination of events, types of distributions, Markov chains, stochastic processes, and more. The book's comprehensive approach provides a complete view of theory along with enlightening examples along the way.

Introduction: The Nature of Probability Theory.
The Sample Space.
Elements of Combinatorial Analysis.
Fluctuations in Coin Tossing and Random Walks.
Combination of Events.
Conditional Probability.
Stochastic Independence.
The Binomial and Poisson Distributions.
The Normal Approximation to the Binomial Distribution.
Unlimited Sequences of Bernoulli Trials.
Random Variables;
Expectation.
Laws of Large Numbers.
Integral Valued Variables.
Generating Functions.
Compound Distributions.
Branching Processes.
Recurrent Events.
Renewal Theory.
Random Walk and Ruin Problems.
Markov Chains.
Algebraic Treatment of Finite Markov Chains.
The Simplest Time-Dependent Stochastic Processes.
Answers to Problems.

William "Vilim" Feller was a Croatian-American mathematician specializing in probability theory.