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• catalog contributor b860513.
• catalog created "[c1965]".
• catalog date "1965".
• catalog date "[c1965]".
• catalog dateCopyrighted "[c1965]".
• catalog description "Includes bibliographical references.".
• catalog description "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.".
• catalog description "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.".
• catalog extent "xi, 583 p.".
• catalog hasFormat "Probability, random variables, and stochastic processes.".
• catalog isFormatOf "Probability, random variables, and stochastic processes.".
• catalog isPartOf "McGraw-Hill series in systems science".
• catalog issued "1965".
• catalog issued "[c1965]".
• catalog language "eng".
• catalog publisher "New York, McGraw-Hill".
• catalog relation "Probability, random variables, and stochastic processes.".
• catalog subject "519.1".
• catalog subject "Probabilities.".
• catalog subject "Probability.".
• catalog subject "QA 273 P218p 1965".
• catalog subject "QA273 .P2".
• catalog subject "Random variables.".
• catalog subject "Stochastic Processes.".
• catalog subject "Stochastic processes.".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog title "Probability, random variables, and stochastic processes.".
• catalog type "text".