Probability, Statistics, and Random Processes for Engineers , 4/e (IE-Paperback)

Henry Stark , John Woods

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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