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[BX0141] Probability, Statistics, and Random Processes for Engineers 4/E    首頁 > 英文圖書類 > Mathes
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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

 本書其它內容…

作(編/譯)者 : STARK 出版年份 : 2012
ISBN : 9780273752288 書號 : BX0141
幾色 : 1 規格 : 平裝
發行公司 : PEARSON 英文書名中譯 : 隨機程序/機率論
版次 : 4E 頁數 : 704
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