Probability Statistics and Random Processes for Engineers 4th Edition by Henry Stark 0132311232 9780132311236

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Product details:

• ISBN 10:0132311232 

• ISBN 13:9780132311236

• Author:Henry Stark 

For courses in Probability and Random Processes. Probability, Statistics, and Random Processes for Engineers, 4e is a useful text for electrical and computer engineers. This book is a comprehensive treatment of probability and random processes that, more than any other available source, combines rigor with accessibility. Beginning with the fundamentals of probability theory and requiring only college-level calculus, the book develops all the tools needed to understand more advanced topics such as random sequences, continuous-time random processes, and statistical signal processing. The book progresses at a leisurely pace, never assuming more knowledge than contained in the material already covered. Rigor is established by developing all results from the basic axioms and carefully defining and discussing such advanced notions as stochastic convergence, stochastic integrals and resolution of stochastic processes.

Probability Statistics and Random Processes for Engineers 4th Table of contents:

 1 Introduction to Probability

• 1.1 Introduction: Why Study Probability?

• 1.2 The Different Kinds of Probability

• 1.3 Misuses, Miscalculations, and Paradoxes in Probability

• 1.4 Sets, Fields, and Events

• 1.5 Axiomatic Definition of Probability

• 1.6 Joint, Conditional, and Total Probabilities; Independence

• 1.7 Bayes’ Theorem and Applications

• 1.8 Combinatorics 38

• 1.9 Bernoulli Trials–Binomial and Multinomial Probability Laws

• 1.10 Asymptotic Behavior of the Binomial Law: The Poisson Law

• 1.11 Normal Approximation to the Binomial Law

2 Random Variables

• 2.1 Introduction

• 2.2 Definition of a Random Variable

• 2.3 Cumulative Distribution Function

• 2.4 Probability Density Function (pdf)

• 2.5 Continuous, Discrete, and Mixed Random Variables

• 2.6 Conditional and Joint Distributions and Densities

• 2.7 Failure Rates

3 Functions of Random Variables

• 3.1 Introduction

• 3.2 Solving Problems of the Type Y = g(X)

• 3.3 Solving Problems of the Type Z = g(X, Y )

• 3.4 Solving Problems of the Type V = g(X, Y ), W = h(X, Y )

• 3.5 Additional Examples

4 Expectation and Moments

• 4.1 Expected Value of a Random Variable

• 4.2 Conditional Expectations

• 4.3 Moments of Random Variables

• 4.4 Chebyshev and Schwarz Inequalities

• 4.5 Moment-Generating Functions

• 4.6 Chernoff Bound

• 4.7 Characteristic Functions

• 4.8 Additional Examples

5 Random Vectors

• 5.1 Joint Distribution and Densities

• 5.2 Multiple Transformation of Random Variables

• 5.3 Ordered Random Variables

• 5.4 Expectation Vectors and Covariance Matrices

• 5.5 Properties of Covariance Matrices

• 5.6 The Multidimensional Gaussian (Normal) Law

• 5.7 Characteristic Functions of Random Vectors

6 Statistics: Part 1 Parameter Estimation

• 6.1 Introduction

• 6.2 Estimators

• 6.3 Estimation of the Mean

• 6.4 Estimation of the Variance and Covariance

• 6.5 Simultaneous Estimation of Mean and Variance

• 6.6 Estimation of Non-Gaussian Parameters from Large Samples

• 6.7 Maximum Likelihood Estimators

• 6.8 Ordering, more on Percentiles, Parametric Versus Nonparametric Statistics

• 6.9 Estimation of Vector Means and Covariance Matrices

• 6.10 Linear Estimation of Vector Parameters

7 Statistics: Part 2 Hypothesis Testing

• 7.1 Bayesian Decision Theory

• 7.2 Likelihood Ratio Test

• 7.3 Composite Hypotheses

• 7.4 Goodness of Fit

• 7.5 Ordering, Percentiles, and Rank

8 Random Sequences

• 8.1 Basic Concepts

• 8.2 Basic Principles of Discrete-Time Linear Systems

• 8.3 Random Sequences and Linear Systems

• 8.4 WSS Random Sequences

• 8.5 Markov Random Sequences

• 8.6 Vector Random Sequences and State Equations

• 8.7 Convergence of Random Sequences

• 8.8 Laws of Large Numbers

9 Random Processes

• 9.1 Basic Definitions

• 9.2 Some Important Random Processes

• 9.3 Continuous-Time Linear Systems with Random Inputs

• 9.4 Some Useful Classifications of Random Processes

• 9.5 Wide-Sense Stationary Processes and LSI Systems

• 9.6 Periodic and Cyclostationary Processes

• 9.7 Vector Processes and State Equations

Appendix A Review of Relevant Mathematics

• A.1 Basic Mathematics

• A.2 Continuous Mathematics

• A.3 Residue Method for Inverse Fourier Transformation

• A.4 Mathematical Induction

Appendix B Gamma and Delta Functions

• B.1 Gamma Function

• B.2 Incomplete Gamma Function

• B.3 Dirac Delta Function

Appendix C Functional Transformations and Jacobians

• C.1 Introduction

• C.2 Jacobians for n = 2

• C.3 Jacobian for General n

Appendix D Measure and Probability

• D.1 Introduction and Basic Ideas

• D.2 Application of Measure Theory to Probability

Appendix E Sampled Analog Waveforms and Discrete-time Signals

Appendix F Independence of Sample Mean and Variance for Normal Random Variables

Appendix G Tables of Cumulative Distribution Functions: the Normal, Student t, Chi-square, and F

Index

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