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

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

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內容描述

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<內容簡介>
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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