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Theoretical Probability for Applications
Throughout Theoretical Probability for Applications the focus is on the practical uses of this increasingly important tool. It develops topics of discrete time probability theory for use in a multitude of applications, including stochastic processes, theoretical statistics, and other disciplines that require a sound foundation in modern probability theory. Principles of measure theory related to the study of probability theory are developed as they are required throughout the book. The book examines most of the basic probability models that involve only a finite or countably infinite number of random variables. Topics in the "Discrete Models" section include Bernoulli trials, random walks, matching, sums of indicators, multinomial trials. Poisson approximations and processes, sampling. Markov chains, and discrete renewal theory. Nondiscrete models discussed include univariate, Beta, sampling, and Dirichlet distributions as well as order statistics.
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Introduction to Probability Theory
Probability spaces; Combinatorial analysis; Discrete random variables; Expectation of discrete random variables; Continuous random variables; Jointly distributed random variables; Expectations and the central limit theorem; Moment generating functions and characteristic functions; Random walks and poisson processes.
Statistics and Decisions
This book provides the necessary prerequisites in probability and statistics as well as the key ideas in decision theory. It is helpful to students and practitioners who desire to apply decision-theoretic thinking to their own work.
Newsletter
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An Introduction to Stochastic Processes
Random walk; Markov chains; Poisson processes; Purely discontinuous markov processes; Calculus with stochastic processes; Stationary processes; Martingales; Brownian motion and diffusion stochastic processes.
