Introduction to Probability Models Sheldon M. Ross

Introduction to Probability Models by Sheldon M. Ross

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A revision of Ross' textbook introducing elementary probability theory and stochastic processes. This edition features updated examples and exercises, with an emphasis wherever possible on real data. There is also new material on Compound Poisson Processes.

Introduction to Probability Models by Sheldon M. Ross

This text is a revision of Ross' textbook introducing elementary probability theory and stochastic processes. The text should be suited to those wanting to apply probability theory to the study of phenomena in fields such as engineering, management science, the physical and social sciences and operations research. This fifth edition features updated examples and exercises, with an emphasis wherever possible on real data. Other changes include new material on Compound Poisson Processes and numerous new applications such as tracking the number of AIDS cases, applications of the reverse chain to queueing networks, and applications of Brownian motion to stock option pricing. This edition also features a complete solutions manual for instructors, as well as a salable partial solutions manual for students.

Part 1 Introduction to probability theory: sample space and events; probabilities defined on events; conditional probabilities; independent events; Bayes' formula. Part 2 Random variables: random variables; discrete random variables - the Bernoulli random variable; the binomial random variable; the geometric random variable; the Poisson random variable; continuous random variables - the uniform random variable; exponential random variables; gamma random variables; normal random variables; expectation of a random variable - the discrete case; the continuous case; expectation of a function of a random variable; jointly distributed random variables - joint distribution functions; independent random variables; joint probability distribution of functions of random variables; moment generating functions; limit theorems; stochastic processes. Part 3 Conditional probability and conditional expectation: the discrete case; the continuous case; computing expectations by conditioning; computing probabilities by conditioning; some applications - a list model; a random graph; uniform priors, Polya's Um model and Bose-Einstein statistics; in normal sampling X and S2 are independent problems. Part 4 Markov chains: Chapman-Kolmogorov equations; classification of states; limiting probabilities; some applications - the Gambler's Ruin problem; a model for algorithmic efficiency; branching processes; time reversible Markov chains; Markov decision processes. Part 5 The exponential distribution and the Poisson process: the exponential distribution - definition; properties of the exponential distribution; further properties of the exponential distribution; the Poisson process - counting processes; definition of the Poisson process; interarrival and waiting time distributions; further properties of Poisson processes; conditional distribution of the arrival times; estimating software reliability; generalizations of the Poisson process - nonhomogeneous Poisson process; compound Poisson process. Part 6 Continuous-time Markov chains: continuous-time Markov chains; birth and death processes; the Kolmogorov differential equations; limiting probabilities; time reversibility; uniformization; computing the transition probabilities. Part 7 Renewal theory and its applications: distribution of N(t); limit theorems and their applications; renewal reward processes. (Part contents)

Introduction to Probability Models Sheldon M. Ross

Introduction to Probability Models by Sheldon M. Ross

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Introduction to Probability Models Summary

Introduction to Probability Models by Sheldon M. Ross

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