Probability, random variables, and random processes [electronic resource] : theory and signal processing applications / John J. Shynk.

Shynk, John Joseph.
Hoboken, NJ : Wiley, 2012, c2013.
1 online resource (796 p.)

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Probabilities -- Textbooks.
Stochastic processes -- Textbooks.
Engineering -- Statistical methods -- Textbooks.
Electronic books.
Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several app
PROBABILITY, RANDOM VARIABLES, AND RANDOM PROCESSES; CONTENTS; PREFACE; NOTATION; 1 Overview and Background; 1.1 Introduction; 1.1.1 Signals, Signal Processing, and Communications; 1.1.2 Probability, Random Variables, and Random Vectors; 1.1.3 Random Sequences and Random Processes; 1.1.4 Delta Functions; 1.2 Deterministic Signals and Systems; 1.2.1 Continuous Time; 1.2.2 Discrete Time; 1.2.3 Discrete-Time Filters; 1.2.4 State-Space Realizations; 1.3 Statistical Signal Processing with MATLABĀ®; 1.3.1 Random Number Generation; 1.3.2 Filtering; Problems; Further Reading
PART I Probability, Random Variables, and Expectation2 Probability Theory; 2.1 Introduction; 2.2 Sets and Sample Spaces; 2.3 Set Operations; 2.4 Events and Fields; 2.5 Summary of a Random Experiment; 2.6 Measure Theory; 2.7 Axioms of Probability; 2.8 Basic Probability Results; 2.9 Conditional Probability; 2.10 Independence; 2.11 Bayes' Formula; 2.12 Total Probability; 2.13 Discrete Sample Spaces; 2.14 Continuous Sample Spaces; 2.15 Nonmeasurable Subsets of R; Problems; Further Reading; 3 Random Variables; 3.1 Introduction; 3.2 Functions and Mappings; 3.3 Distribution Function
3.4 Probability Mass Function3.5 Probability Density Function; 3.6 Mixed Distributions; 3.7 Parametric Models for Random Variables; 3.8 Continuous Random Variables; 3.8.1 Gaussian Random Variable (Normal); 3.8.2 Log-Normal Random Variable; 3.8.3 Inverse Gaussian Random Variable (Wald); 3.8.4 Exponential Random Variable (One-Sided); 3.8.5 Laplace Random Variable (Double-Sided Exponential); 3.8.6 Cauchy Random Variable; 3.8.7 Continuous Uniform Random Variable; 3.8.8 Triangular Random Variable; 3.8.9 Rayleigh Random Variable; 3.8.10 Rice Random Variable
3.9.3 Geometric Random Variable (with Support Z+ or N)3.9.4 Negative Binomial Random Variable (Pascal); 3.9.5 Poisson Random Variable; 3.9.6 Hypergeometric Random Variable; 3.9.7 Discrete Uniform Random Variable; 3.9.8 Logarithmic Random Variable (Log-Series); 3.9.9 Zeta Random Variable (Zipf); Problems; Further Reading; 4 Multiple Random Variables; 4.1 Introduction; 4.2 Random Variable Approximations; 4.2.1 Binomial Approximation of Hypergeometric; 4.2.2 Poisson Approximation of Binomial; 4.2.3 Gaussian Approximations; 4.2.4 Gaussian Approximation of Binomial
4.2.5 Gaussian Approximation of Poisson
Description based upon print version of record.
Includes bibliographical references and index.