{"product_id":"introduction-to-probability-theory-and-stochastic-processes-isbn-9781118382790","title":"Introduction to Probability Theory and Stochastic Processes","description":"\u003cp\u003e\u003cb\u003eA unique approach to stochastic processes that connects the mathematical formulation of random processes to their use in applications\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis book presents an innovative approach to teaching probability theory and stochastic processes based on the binary expansion of the unit interval. Departing from standard pedagogy, it uses the binary expansion of the unit interval to explicitly construct an infinite sequence of independent random variables (of any given distribution) on a single probability space. This construction then provides the framework to understand the mathematical formulation of probability theory for its use in applications.\u003c\/p\u003e \u003cp\u003eFeatures include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eThe theory is presented first for countable sample spaces (Chapters 1-3) and then for uncountable sample spaces (Chapters 4-18)\u003c\/li\u003e \u003cli\u003eCoverage of the explicit construction of i.i.d. random variables on a single probability space to explain why it is the distribution function rather than the functional form of random variables that matters when it comes to modeling random phenomena\u003c\/li\u003e \u003cli\u003eExplicit construction of continuous random variables to facilitate the \"digestion\" of random variables, i.e., how they are used in contrast to how they are defined\u003c\/li\u003e \u003cli\u003eExplicit construction of continuous random variables to facilitate the two views of \u003ci\u003eexpectation:\u003c\/i\u003e as integration over the underlying probability space (abstract view) or as integration using the density function (usual view)\u003c\/li\u003e \u003cli\u003eA discussion of the connections between Bernoulli, geometric, and Poisson processes\u003c\/li\u003e \u003cli\u003eIncorporation of the Johnson-Nyquist noise model and an explanation of why (and when) it is valid to use a delta function to model its autocovariance\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eComprehensive, astute, and practical, \u003ci\u003eIntroduction to Probability Theory and Stochastic Processes\u003c\/i\u003e is a clear presentation of essential topics for those studying communications, control, machine learning, digital signal processing, computer networks, pattern recognition, image processing, and coding theory.\u003c\/p\u003e \u003cp\u003e1 Coin Tossing 1\u003c\/p\u003e \u003cp\u003e2 Countable Sample Spaces 61\u003c\/p\u003e \u003cp\u003e3 Conditional Probability in Countable Sample Spaces 105\u003c\/p\u003e \u003cp\u003e4 Uncountable Sample Spaces 151\u003c\/p\u003e \u003cp\u003e5 Continuous Random Variables 213\u003c\/p\u003e \u003cp\u003e6 Expectation 245\u003c\/p\u003e \u003cp\u003e7 Modeling Random Phenomena 267\u003c\/p\u003e \u003cp\u003e8 Functions of One Random Variables and Transforms 321\u003c\/p\u003e \u003cp\u003e9 Functions of Two Random Variables 365\u003c\/p\u003e \u003cp\u003e10 Two Functions of Two Random Variables 431\u003c\/p\u003e \u003cp\u003e11 Conditional Probability for Continuous Random Variables 473\u003c\/p\u003e \u003cp\u003e12 Random Vectors 549\u003c\/p\u003e \u003cp\u003e13 Bernoulli, Geometric, and Poisson Processes 587\u003c\/p\u003e \u003cp\u003e14 Brownian Motions and White Noise 645\u003c\/p\u003e \u003cp\u003e15 Stationary Random Processes 703\u003c\/p\u003e \u003cp\u003e16 Convergence of Random Variables 777\u003c\/p\u003e \u003cp\u003e17 Statistics 839\u003c\/p\u003e \u003cp\u003e18 Kalman Filter 905\u003c\/p\u003e \u003cp\u003eFurther Reading 933\u003c\/p\u003e \u003cp\u003eTable of Common Distributions 935\u003c\/p\u003e \u003cp\u003eReferences 941\u003c\/p\u003e \u003cp\u003eIndex 946\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eJOHN CHIASSON, PhD,\u003c\/b\u003e is a Fellow of the IEEE and the author of \u003ci\u003eModeling and High-Performance Control of Electric Machines,\u003c\/i\u003e published by Wiley-IEEE Press.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eA unique approach to stochastic processes that connects the mathematical formulation of random processes to their use in applications\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis book presents an innovative approach to teaching probability theory and stochastic processes based on the binary expansion of the unit interval. Departing from standard pedagogy, it uses the binary expansion of the unit interval to explicitly construct an infinite sequence of independent random variables (of any given distribution) on a single probability space. This construction then provides the framework to understand the mathematical formulation of probability theory for its use in applications.\u003c\/p\u003e \u003cp\u003eFeatures include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eThe theory is presented first for countable sample spaces (Chapters 1-3) and then for uncountable sample spaces (Chapters 4-18)\u003c\/li\u003e \u003cli\u003eCoverage of the explicit construction of i.i.d. random variables on a single probability space to explain why it is the distribution function rather than the functional form of random variables that matters when it comes to modeling random phenomena\u003c\/li\u003e \u003cli\u003eExplicit construction of continuous random variables to facilitate the \"digestion\" of random variables, i.e., how they are used in contrast to how they are defined\u003c\/li\u003e \u003cli\u003eExplicit construction of continuous random variables to facilitate the two views of \u003ci\u003eexpectation:\u003c\/i\u003e as integration over the underlying probability space (abstract view) or as integration using the density function (usual view)\u003c\/li\u003e \u003cli\u003eA discussion of the connections between Bernoulli, geometric, and Poisson processes\u003c\/li\u003e \u003cli\u003eIncorporation of the Johnson-Nyquist noise model and an explanation of why (and when) it is valid to use a delta function to model its autocovariance\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eComprehensive, astute, and practical, \u003ci\u003eIntroduction to Probability Theory and Stochastic Processes\u003c\/i\u003e is a clear presentation of essential topics for those studying communications, control, machine learning, digital signal processing, computer networks, pattern recognition, image processing, and coding theory.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989465284837,"sku":"NP9781118382790","price":125.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118382790.jpg?v=1761784209","url":"https:\/\/k12savings.com\/products\/introduction-to-probability-theory-and-stochastic-processes-isbn-9781118382790","provider":"K12savings","version":"1.0","type":"link"}