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The Resource Probability, random variables, and stochastic processes

Probability, random variables, and stochastic processes

Label
Probability, random variables, and stochastic processes
Title
Probability, random variables, and stochastic processes
Creator
Subject
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1921-2002
http://library.link/vocab/creatorName
Papoulis, Athanasios
Illustrations
illustrations
Index
no index present
Literary form
non fiction
Series statement
McGraw-Hill series in systems science
http://library.link/vocab/subjectName
  • Probabilities
  • Random variables
  • Stochastic processes
  • Probability
Label
Probability, random variables, and stochastic processes
Instantiates
Publication
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 ; Mean-square estimation, the orthogonality principle ; More on normal random variables -- Sequences of random variables: General concepts ; Mean, mean-square estimation, moments, characteristic functions ; Applications ; Normal random variables ; Convergence concepts and the law of large numbers ; The central-limit 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 ; Mean-square periodicity and Fourier series ; Band-limited processes ; An estimate of the variation of a band-limited process -- Linear mean-square estimation: Introductory remarks ; The orthogonality principle in linear mean-square estimation ; The Wiener-Kolmogoroff theory ; The filtering problem ; The prediction problem ; Wide-sense Markoff sequences and recursive filtering -- Nonstationary processes; transients in linear systems with stochastic inputs: Transients in linear systems with stochastic inputs ; Two-dimensional 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 zero-crossing problem ; Conditional densities and mean-square estimation ; Bandpass processes ; The Wiener-Levy 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 ; High-density shot noise ; Square-law 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
Publication
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 ; Mean-square estimation, the orthogonality principle ; More on normal random variables -- Sequences of random variables: General concepts ; Mean, mean-square estimation, moments, characteristic functions ; Applications ; Normal random variables ; Convergence concepts and the law of large numbers ; The central-limit 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 ; Mean-square periodicity and Fourier series ; Band-limited processes ; An estimate of the variation of a band-limited process -- Linear mean-square estimation: Introductory remarks ; The orthogonality principle in linear mean-square estimation ; The Wiener-Kolmogoroff theory ; The filtering problem ; The prediction problem ; Wide-sense Markoff sequences and recursive filtering -- Nonstationary processes; transients in linear systems with stochastic inputs: Transients in linear systems with stochastic inputs ; Two-dimensional 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 zero-crossing problem ; Conditional densities and mean-square estimation ; Bandpass processes ; The Wiener-Levy 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 ; High-density shot noise ; Square-law 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

Library Locations

    • Mathematical Sciences LibraryBorrow it
      104 Ellis Library, Columbia, MO, 65201, US
      38.944377 -92.326537
    • Engineering Library & Technology CommonsBorrow it
      W2001 Lafferre Hall, Columbia, MO, 65211, US
      38.946102 -92.330125
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