Probability and Random Processes

The second edition enhanced with new chapters, figures, and appendices to cover the new developments in applied mathematical functions

This book examines the topics of applied mathematical functions to problems that engineers and researchers solve daily in the course of their work. The text covers set theory, combinatorics, random variables, discrete and continuous probability, distribution functions, convergence of random variables, computer generation of random variates, random processes and stationarity concepts with associated autocovariance and cross covariance functions, estimation theory and Wiener and Kalman filtering ending with two applications of probabilistic methods. Probability tables with nine decimal place accuracy and graphical Fourier transform tables are included for quick reference. The author facilitates understanding of probability concepts for both students and practitioners by presenting over 450 carefully detailed figures and illustrations, and over 350 examples with every step explained clearly and some with multiple solutions.

Additional features of the second edition of Probability and Random Processes are:

• Updated chapters with new sections on Newton-Pepys’ problem; Pearson, Spearman, and Kendal correlation coefficients; adaptive estimation techniques; birth and death processes; and renewal processes with generalizations
• A new chapter on Probability Modeling in Teletraffic Engineering written by Kavitha Chandra
• An eighth appendix examining the computation of the roots of discrete probability-generating functions

With new material on theory and applications of probability, Probability and Random Processes, Second Edition is a thorough and comprehensive reference for commonly occurring problems in probabilistic methods and their applications.

Avainsanat:

Lattice theory; Combinatorics; Bayes’ Theorem; Bernoulli Trials; Discrete Distributions; Newton-Pepys Problem; Gaussian Distribution; Bivariate Gaussian Distributions; Continuous Distributions; Boolean Algebra; Chebyshev’s Inequality; Markov Inequality; Chernoff Bound; Cauchy-Schwartz Inequality; Random Processes; Poisson Process; Binomial Process; Wiener Process; Periodic Random Process; Aperiodic Random Process; Orthogonality Principle; Wiener Filtering; Kalman Filters; Teletraffic Engineering; Stochastic Estimation Algorithm; Fourier Transform