The Resource Probability, random variables, and stochastic processes
Probability, random variables, and stochastic processes
Resource Information
The item Probability, random variables, and stochastic processes represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 2 library branches.
Resource Information
The item Probability, random variables, and stochastic processes represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 2 library branches.
 Language
 eng
 Extent
 xi, 583 pages
 Contents

 Probability and random variables. The meaning of probability: Preliminary remarks ; The various definitions of probability ; Determinism versus probability  The axioms of probability: Set theory ; Probability space ; Conditional probabilities and independent events ; Summary  Repeated trials: Combined experiments ; Bernoulli trials ; Asymptotic theorems ; Generalized Bernoulli trials ; Bayes' theorem in statistics  The concept of a random variable: Random variables, distributions, densities ; Examples of distribution and density functions ; Conditional distributions and densities ; Bayes' theorem in statistics (reexamined)  Functions of one random variable: The concept of a function of one random variable ; Determination of the distribution and density of y = g(x) ; Applications ; Expected value, dispersion, moments ; Characteristic functions  Two random variables: Joint distribution and density functions ; Conditional distributions and densities ; Independent random variables ; Jointly normal random variables  Functions of two random variables: One function of two random variables ; Two functions of two random variables ; Expected value, moments, characteristic functions ; Meansquare estimation, the orthogonality principle ; More on normal random variables  Sequences of random variables: General concepts ; Mean, meansquare estimation, moments, characteristic functions ; Applications ; Normal random variables ; Convergence concepts and the law of large numbers ; The centrallimit theorem
 Stochastic processes. General concepts: Introduction remarks ; Special processes ; Definitions ; Stationary processes ; Transformation of stochastic processes (systems) ; Stochastic continuity and differentiation ; Stochastic differential equations ; Stochastic integrals, time averages, ergodicity  Correlation and power spectrum of stationary processes: Correlation ; Power spectrum ; Linear systems ; Hilbert transforms, shot noise, thermal noise ; Meansquare periodicity and Fourier series ; Bandlimited processes ; An estimate of the variation of a bandlimited process  Linear meansquare estimation: Introductory remarks ; The orthogonality principle in linear meansquare estimation ; The WienerKolmogoroff theory ; The filtering problem ; The prediction problem ; Widesense Markoff sequences and recursive filtering  Nonstationary processes; transients in linear systems with stochastic inputs: Transients in linear systems with stochastic inputs ; Twodimensional Fourier transforms ; Time averages  Harmonic analysis of stochastic processes: Series expansions ; Approximate Fourier expansion with uncorrelated coefficients ; Fourier transforms of stochastic processes ; Generalized harmonic analysis  Stationary and nonstationary normal processes: General remarks ; Stationary processes ; Detection ; The zerocrossing problem ; Conditional densities and meansquare estimation ; Bandpass processes ; The WienerLevy process  Brownian movement and Markoff processes: Langevin's equation ; Motion of a harmonically bound particle ; Markoff sequences ; Markoff processes  Poisson process and shot noise: Poisson distributions ; Random points in time ; Shot noise ; Densities and characteristic functions ; Highdensity shot noise ; Squarelaw detection of shot noise
 Label
 Probability, random variables, and stochastic processes
 Title
 Probability, random variables, and stochastic processes
 Language
 eng
 Cataloging source
 DLC
 http://library.link/vocab/creatorDate
 19212002
 http://library.link/vocab/creatorName
 Papoulis, Athanasios
 Illustrations
 illustrations
 Index
 no index present
 Literary form
 non fiction
 Series statement
 McGrawHill series in systems science
 http://library.link/vocab/subjectName

 Probabilities
 Random variables
 Stochastic processes
 Probability
 Label
 Probability, random variables, and stochastic processes
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Probability and random variables. The meaning of probability: Preliminary remarks ; The various definitions of probability ; Determinism versus probability  The axioms of probability: Set theory ; Probability space ; Conditional probabilities and independent events ; Summary  Repeated trials: Combined experiments ; Bernoulli trials ; Asymptotic theorems ; Generalized Bernoulli trials ; Bayes' theorem in statistics  The concept of a random variable: Random variables, distributions, densities ; Examples of distribution and density functions ; Conditional distributions and densities ; Bayes' theorem in statistics (reexamined)  Functions of one random variable: The concept of a function of one random variable ; Determination of the distribution and density of y = g(x) ; Applications ; Expected value, dispersion, moments ; Characteristic functions  Two random variables: Joint distribution and density functions ; Conditional distributions and densities ; Independent random variables ; Jointly normal random variables  Functions of two random variables: One function of two random variables ; Two functions of two random variables ; Expected value, moments, characteristic functions ; Meansquare estimation, the orthogonality principle ; More on normal random variables  Sequences of random variables: General concepts ; Mean, meansquare estimation, moments, characteristic functions ; Applications ; Normal random variables ; Convergence concepts and the law of large numbers ; The centrallimit theorem
 Stochastic processes. General concepts: Introduction remarks ; Special processes ; Definitions ; Stationary processes ; Transformation of stochastic processes (systems) ; Stochastic continuity and differentiation ; Stochastic differential equations ; Stochastic integrals, time averages, ergodicity  Correlation and power spectrum of stationary processes: Correlation ; Power spectrum ; Linear systems ; Hilbert transforms, shot noise, thermal noise ; Meansquare periodicity and Fourier series ; Bandlimited processes ; An estimate of the variation of a bandlimited process  Linear meansquare estimation: Introductory remarks ; The orthogonality principle in linear meansquare estimation ; The WienerKolmogoroff theory ; The filtering problem ; The prediction problem ; Widesense Markoff sequences and recursive filtering  Nonstationary processes; transients in linear systems with stochastic inputs: Transients in linear systems with stochastic inputs ; Twodimensional Fourier transforms ; Time averages  Harmonic analysis of stochastic processes: Series expansions ; Approximate Fourier expansion with uncorrelated coefficients ; Fourier transforms of stochastic processes ; Generalized harmonic analysis  Stationary and nonstationary normal processes: General remarks ; Stationary processes ; Detection ; The zerocrossing problem ; Conditional densities and meansquare estimation ; Bandpass processes ; The WienerLevy process  Brownian movement and Markoff processes: Langevin's equation ; Motion of a harmonically bound particle ; Markoff sequences ; Markoff processes  Poisson process and shot noise: Poisson distributions ; Random points in time ; Shot noise ; Densities and characteristic functions ; Highdensity shot noise ; Squarelaw detection of shot noise
 Control code
 527708
 Dimensions
 23 cm
 Extent
 xi, 583 pages
 Lccn
 64022956
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 System control number
 (WaOLN)356813
 Label
 Probability, random variables, and stochastic processes
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Probability and random variables. The meaning of probability: Preliminary remarks ; The various definitions of probability ; Determinism versus probability  The axioms of probability: Set theory ; Probability space ; Conditional probabilities and independent events ; Summary  Repeated trials: Combined experiments ; Bernoulli trials ; Asymptotic theorems ; Generalized Bernoulli trials ; Bayes' theorem in statistics  The concept of a random variable: Random variables, distributions, densities ; Examples of distribution and density functions ; Conditional distributions and densities ; Bayes' theorem in statistics (reexamined)  Functions of one random variable: The concept of a function of one random variable ; Determination of the distribution and density of y = g(x) ; Applications ; Expected value, dispersion, moments ; Characteristic functions  Two random variables: Joint distribution and density functions ; Conditional distributions and densities ; Independent random variables ; Jointly normal random variables  Functions of two random variables: One function of two random variables ; Two functions of two random variables ; Expected value, moments, characteristic functions ; Meansquare estimation, the orthogonality principle ; More on normal random variables  Sequences of random variables: General concepts ; Mean, meansquare estimation, moments, characteristic functions ; Applications ; Normal random variables ; Convergence concepts and the law of large numbers ; The centrallimit theorem
 Stochastic processes. General concepts: Introduction remarks ; Special processes ; Definitions ; Stationary processes ; Transformation of stochastic processes (systems) ; Stochastic continuity and differentiation ; Stochastic differential equations ; Stochastic integrals, time averages, ergodicity  Correlation and power spectrum of stationary processes: Correlation ; Power spectrum ; Linear systems ; Hilbert transforms, shot noise, thermal noise ; Meansquare periodicity and Fourier series ; Bandlimited processes ; An estimate of the variation of a bandlimited process  Linear meansquare estimation: Introductory remarks ; The orthogonality principle in linear meansquare estimation ; The WienerKolmogoroff theory ; The filtering problem ; The prediction problem ; Widesense Markoff sequences and recursive filtering  Nonstationary processes; transients in linear systems with stochastic inputs: Transients in linear systems with stochastic inputs ; Twodimensional Fourier transforms ; Time averages  Harmonic analysis of stochastic processes: Series expansions ; Approximate Fourier expansion with uncorrelated coefficients ; Fourier transforms of stochastic processes ; Generalized harmonic analysis  Stationary and nonstationary normal processes: General remarks ; Stationary processes ; Detection ; The zerocrossing problem ; Conditional densities and meansquare estimation ; Bandpass processes ; The WienerLevy process  Brownian movement and Markoff processes: Langevin's equation ; Motion of a harmonically bound particle ; Markoff sequences ; Markoff processes  Poisson process and shot noise: Poisson distributions ; Random points in time ; Shot noise ; Densities and characteristic functions ; Highdensity shot noise ; Squarelaw detection of shot noise
 Control code
 527708
 Dimensions
 23 cm
 Extent
 xi, 583 pages
 Lccn
 64022956
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 System control number
 (WaOLN)356813
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