Probability and random processes : an introduction for applied scientists and engineers /

Probability and random processes : an introduction for applied scientists and engineers /

Preface, This book, intended as a text for a first course in probability and random processes, can be used either for self-study or in a formal classroom setting.In the classroom context, the first eight chapters could form a one-semester subject on probability with the last six chapters (plus posib...

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Detalles Bibliográficos
Formato: Libro
Lenguaje:Spanish
Publicado: Japan : McGraw-Hill, ©1970
Tabla de Contenidos:
  • 1. Introduction. 1 Randomness and averages.
  • 2 Empirical averages.
  • 3 Relative frequency.
  • 4 Stability.
  • 5 Probability and statistical averages. – 6 Summary and preview. – References.
  • 2. Sample points and sample spaces. 1 Introduction.
  • 2 Events.
  • 3 Algebra of events.
  • 4 Partilions.
  • 5 Sequences of events. – 6 Summary of definitons and formulas.
  • References.
  • 3. Probability. 1 Probabilily axioms.
  • 2 Elementary properties of probability.
  • 3 Probability spaces. – 4 The continuity theorem of probability.
  • 5 Joint probability.
  • 6 Conditional probability. – 7 Independent events.
  • 8 Independent experiments. – 9 Summary of axioms, definitions, and formulas.
  • References.
  • 4. Random variables.
  • 5. Random vectors. 1 Random variables.
  • 2 Probability distributions, densities, and distribution functions.
  • 3 Properties of probability distribution functions.
  • 4 Derivations.
  • 5 Probability densities.
  • 6 Mixed random variables.
  • 7 Summary of definitions and formulas. – References.
  • 6. Functions of random variables. 1 Introduction.
  • 2 Functions of random variables.
  • 3 Functions of random vectors. – 4 One-to-one transformations.
  • 5 Summary. – References.
  • 7. Statistical averages. 1 Discrete random variables.
  • 2 Eristence (discrete case).
  • 3 Functions of discrete random variables.
  • 4 Functions of discrele random vectors.
  • 5 Extension to the continuous case.
  • 6 Continuous-case examples and exercises.
  • 7 Existence (continuous case).
  • 8 Moments.
  • 9 Joint moments.
  • 10 Gaussian random vectors.
  • 11 Conditional averages. – 12 Inequalities.
  • 13 Summary of definitions and formulas. – References.
  • 8. Estimation, sampling, and prediction. 1 Introduction.
  • 2 The sample mean. – 3 Relative frequency.
  • 4 Relative frequency (continued). – 5 Minimum-variance estimators. – 6 Prediction.
  • 7 Linear prediction.
  • 8 Summary of definitions and formulas. – References.
  • 9. Random processes. 1 Bernoulli process.
  • 2 Binomial process.
  • 3 Sine wave process. – 4 Random process descriptions.
  • 5 Stationarity.
  • 6 Covariance and correlation functions.
  • 7 Stationarily (continued).
  • 8 Sampling a random process.
  • 9 Periodic sampling.
  • 10 Summary of definitions and formulas. – References.
  • 10. Linear transformations. 1 Two-dimensional vectors.
  • 2 N-dimensional vectors.
  • 3 Matrix formulation. – 4 Time averages. – 5 Weighting functions. – 6 Output moments.
  • 7 Summary of definitions and formulas.
  • References.
  • 11. Spectral analysis. 1 Introduction.
  • 2 Sine wave in, sine wave out.
  • 3 Fourier analysis.
  • 4 Spectral density.
  • 5 Some general properties of the spectral density.
  • 6 Spectral analysis of linear Systems.
  • 7 Narrowband filtering.
  • 8 Cross-Spectral densities.
  • 9 Epilogue.
  • 10 Summary of definitions and formulas. – References.
  • 12. Sums of independent random variables. 1 Introduction.
  • 2 Independent increment processes.
  • 3 Linear-functional equation. – 4 Characteristic function. – 5 Further properties of the characteristic function.
  • 6 Joint-characteristic functions.
  • 7 Independent increment processes (continued).
  • 8 Probability generating functions.
  • 9 Central limit theorem.
  • 10 Summary of definitions and formulas.
  • References.
  • 13. The poisson process. 1 Introduction.
  • 2 Poisson counting process.
  • 3 Arrival times.
  • 4 Interarrival times.
  • 5 Renewal counting process.
  • 6 Unordered arrival times.
  • 7 Filtered poisson processes.
  • 8 Random partitioning.
  • 9 Summary of definitions and formula. – References.
  • 14. Tha gaussian process. 1 Introduction.
  • 2 Gaussian Random Vectors.
  • 3 Gaussian Random Processes.
  • 4 Narrowband Waveforms.
  • 5 Narrowband Random Processes.
  • 6 Narrowband Gaussian Processes.
  • 7 Summary Of Definitions And Formulas. – References. – Bibliography. – Index.

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