issuhub.com

Fundamentals of Probability and Statistics for Engineers

(John Hannent) #1

  • 1 INTRODUCTION PREFACE xiii

    • 1.1 Organization of Text

    • 1.2 Probability Tables and Computer Software

    • 1.3 Prerequisites



  • PART A: PROBABILITY AND RANDOM VARIABLES

  • 2 BASIC PROBABILITY CONCEPTS

    • 2.1 Elements of Set Theory

      • 2.1.1 Set Operations



    • 2.2 Sample Space and Probability M easure

      • 2.2.1 Axioms of Probability

      • 2.2.2 Assignment of Probability



    • 2.3 Statistical Independence

    • 2.4 Conditional Probability

    • Reference

    • Further Reading

    • Problems

    • DISTRIBUTIONS 3 RANDOM VARIABLES AND PROBABILITY

    • 3.1 Random Variables

    • 3.2 Probability D istributions

      • 3.2.1 Probability D istribution F unction

        • Variables 3.2.2 Probability M ass F unction for D iscrete R andom

        • Variables 3.2.3 Probability D ensity F unction for Continuous Random



      • 3.2.4 M ixed-Type D istribution



    • 3.3 Two or More Random Variables

      • 3.3.1 Joint Probability D istribution F unction

      • 3.3.2 Joint Probability M ass F unction

      • 3.3.3 Joint Probability D ensity F unction



    • 3.4 Conditional Distribution and Independence

    • Further Reading and Comments

    • Problems



  • 4 EXPECTATIONS AND MOMENTS

    • 4.1 Moments of a Single Random Variable

      • 4.1.1 Mean, Median, and Mode

      • 4.1.2 Central Moments, Variance, and Standard Deviation

      • 4.1.3 Conditional Expectation



    • 4.2 Chebyshev Inequality

    • 4.3 Moments of Two or More Random Variables

      • 4.3.1 Covariance and Correlation Coefficient

      • 4.3.2 Schwarz Inequality

      • 4.3.3 The Case of Three or More Random Variables



    • 4.4 Moments of Sums of Random Variables

    • 4.5 Characteristic Functions

      • 4.5.1 G eneration of M oments

      • 4.5.2 Inversion Formulae

      • 4.5.3 Joint Characteristic Functions



    • Further Reading and Comments

    • Problems



  • 5 FUNCTIONS OF RANDOM VARIABLES

    • 5.1 Functions of One Random Variable

      • 5.1.1 Probability D istribution

      • 5.1.2 M oments



    • 5.2 Functions of Two or More Random Variables

      • 5.2.1 Sums of Random Variables



    • 5.3 m Functions of n Random Variables

    • Reference

    • Problems



  • 6 SOME IMPORTANT DISCRETE DISTRIBUTIONS

    • 6.1 Bernoulli Trials

      • 6.1.1 Binomial D istribution

      • 6.1.2 G eometric D istribution

      • 6.1.3 N egative Binomial D istribution



    • 6.2 M ultinomial D istribution

    • 6.3 Poisson D istribution

      • 6.3.1 Spatial Distributions

      • 6.3.2 The Poisson Approximation to the Binomial Distribution



    • 6.4 Summary

    • Further Reading

    • Problems



  • 7 SOME IMPORTANT CONTINUOUS DISTRIBUTIONS

    • 7.1 Uniform Distribution

      • 7.1.1 Bivariate Uniform Distribution



    • 7.2 Gaussian or Normal Distribution

      • 7.2.1 The Central Limit Theorem

      • 7.2.2 Probability Tabulations

      • 7.2.3 Multivariate Normal Distribution

      • 7.2.4 Sums of Normal Random Variables



    • 7.3 Lognormal Distribution

      • 7.3.1 Probability Tabulations



    • 7.4 Gamma and Related Distributions

      • 7.4.1 Exponential Distribution

      • 7.4.2 Chi-Squared Distribution



    • 7.5 Beta and R elated D istributions

      • 7.5.1 Probability Tabulations

      • 7.5.2 G eneralized Beta D istribution



    • 7.6 Extreme-Value Distributions

      • 7.6.1 Type-I Asymptotic Distributions of Extreme Values

      • 7.6.2 Type-II Asymptotic Distributions of Extreme Values

      • 7.6.3 Type-III Asymptotic Distributions of Extreme Values



    • 7.7 Summary

    • R eferences

    • Further Reading and Comments

    • Problems



  • ESTIMATION, AND MODEL VERIFICATION PART B: STATISTICAL INFERENCE, PARAMETER

  • 8 OBSERVED DATA AND GRAPHICAL REPRESENTATION

    • 8.1 Histogram and Frequency Diagrams

    • R eferences

    • Problems



  • 9 PARAMETER ESTIMATION

    • 9.1 Samples and Statistics

      • 9.1.1 Sample M ean

      • 9.1.2 Sample Variance

      • 9.1.3 Sample M oments

      • 9.1.4 Order Statistics



    • 9.2 Quality Criteria for Estimates

      • 9.2.1 U nbiasedness

      • 9.2.2 M inimum Variance

      • 9.2.3 Consistency

      • 9.2.4 Sufficiency



    • 9.3 M ethods of Estimation

      • 9.3.1 Point Estimation

      • 9.3.2 Interval Estimation



    • References

    • Further Reading and Comments

    • Problems



  • 10 MODEL VERIFICATION

    • 10.1 Preliminaries

      • 10.1.1 Type-I and Type-II Errors



    • 10.2 Chi-Squared Goodness-of-Fit Test

      • 10.2.1 The Case of K nown Parameters

      • 10.2.2 The Case of Estimated Parameters



    • 10.3 Kolmogorov–Smirnov Test

    • References

    • Further Reading and Comments

    • Problems



  • 11 LINEAR MODELS AND LINEAR REGRESSION

    • 11.1 Simple Linear R egression

      • 11.1.1 Least Squares M ethod of Estimation

      • 11.1.2 Properties of Least-Square Estimators

      • 11.1.3 U nbiased Estimator for

      • 11.1.4 Confidence Intervals for R egression Coefficients

      • 11.1.5 Significance Tests



    • 11.2 M ultiple Linear R egression

      • 11.2.1 Least Squares M ethod of Estimation



    • 11.3 Other R egression M odels

    • Reference

    • Further Reading

    • Problems



  • APPENDIX A: TABLES

  • A.1 Binomial Mass Function

  • A.2 Poisson Mass Function

  • A.3 Standardized Normal Distribution Function

  • A.4 Student’s t Distribution with n Degrees of Freedom

  • A.5 Chi-Squared Distribution with n Degrees of Freedom

  • A.6 D 2 Distribution with Sample Size n

  • R eferences

  • APPENDIX B: COMPUTER SOFTWARE

  • APPENDIX C: ANSWERS TO SELECTED PROBLEMS

  • Chapter

  • Chapter

  • Chapter

  • Chapter

  • Chapter

  • Chapter

  • Chapter

  • Chapter

  • Chapter

  • Chapter

  • SUBJECT INDEX

Free download pdf
Get our desktop app
Company
Features
Documentation
Resources
© ISSUHUB. 2024. All rights reserved.