Probability and statistics for scientists and engineers / Rao V. Dukkipati.

Format:

Book

Author/Creator:

Dukkipati, Rao V., author.

Language:

English

Subjects (All):

Engineering mathematics.

Probabilities.

Mathematical statistics.

Physical Description:

1 online resource (568 p.)

Edition:

1st ed.

Place of Publication:

Kent, [England] : New Academic Science Limited, 2013.

Language Note:

English

Summary:

Coverage of all course fundamentals in easy-to-understand methodology. Clarity in the presentation of concepts Review questions, true/false, and fill in the blanks for each chapter. Over 230 fully solved problems with step-by-step solutions Over 520 additional practice problems with answers

Contents:

Cover

Preface

Acknowledgements

Contents

Chapter 1 Numerical Descriptive Measures

1.1 Introduction

1.1.1 Population and Sample

1.1.2 Types of Variables

1.1.3 Organising Data

1.1.3.1 Qualitative Data

1.1.3.2 Graphical Representation of Qualitative Data

1.1.3.3 Graphical Representation of Quantitative Data

1.2 Numerical Summary Measures

1.2.1 Measures of Central Tendency for Ungrouped Data

1.2.1.1 Mean for Ungrouped Data

1.2.1.2 Median

1.2.1.3 Mode

1.2.1.4 Empirical Relation among Mean, Median and Mode

1.2.2 Measures of Dispersion for Ungrouped Data

1.2.2.1 Range

1.2.2.2 Variance and Standard Deviation

1.2.3 Mean, Variance and Standard Deviation for Grouped Data

1.2.3.1 Mean for Grouped Data

1.2.3.2 Variance and Standard Deviation for Grouped Data

1.2.4 Measures of Position

1.2.4.1 Quartiles and Interquartile Range

1.2.4.2 Percentiles

1.2.4.3 Skewness and Kurtosis

1.2.4.4 Box-and-Whisker Plot

1.3 Summary

Problems

Review Questions

State True or False

Answers to State True or False

Chapter 2 Probability

2.1 Experiment, Outcome and Sample Space

2.2 Simple and Composite Events

2.3 Axioms of Probability

2.4 Finite Probability Spaces

2.5 Infinite Probability Spaces

2.6 Properties of Probability

2.7 Venn Diagram

2.8 Probability Tree or Tree Diagram

2.9 Approaches to Probability

2.9.1 Classical Probability

2.9.2 Relative Frequency Concept of Probability

2.9.3 Subjective Probability

2.9.4 Marginal Probability

2.9.5 Conditional Probability

2.10 Mutually Exclusive Events

2.11 Independent and Dependent Events

2.12 Complementary Events

2.13 Intersection of Events and Multiplication Rule

2.13.1 Intersection of Events

2.13.2 Multiplication Rule

2.14 Union of Events and the Addition Rule.

2.14.1 Union of Events

2.14.2 Addition Rule

2.15 Baye's Formula

2.16 Additional Examples and Solutions

2.17 Summary

Chapter 3 Random Variables and Probability Distributions

3.1 Random Variables

3.1.1 Discrete Random Variables

3.1.2 Mean and Standard Deviation of a Discrete Random Variable

3.1.3 Continuous Random Variables

3.1.4 Mean and Variance for Continuous Random Variables

3.1.5 Expectation

3.2 Permutations and Combinations

3.2.1 Permutations

3.2.2 Combinations

3.3 Discrete Distributions

3.3.1 Hypergeometric Distribution

3.3.2 The Binomial Probability Distribution

3.3.3 The Binomial Experiment

3.3.4 The Binomial Formula

3.3.4.1 Binomial Theorem

3.3.4.2 Cumulative Terms for Binomial Distribution

3.3.4.3 Mean and Standard Deviation of Binomial Distribution

3.3.5 Poisson Distribution

3.3.5.1 Derivation from Binomial Distribution

3.3.5.2 Mean and Standard Deviation

3.4 Continuous Probability Distributions

3.4.1 The Normal Distribution

3.4.1.1 Properties of the Normal Distribution

3.4.1.2 Mean and Variance of the Normal Distribution

3.4.1.3 The Cumulative Normal Distribution

3.4.1.4 The Standard Normal Distribution

3.4.1.5 Problem-Solving Procedure

3.5 Approximating Probability Distributions

3.5.1 Binomial Approximation to the Hypergeometric

3.5.2 Poisson Approximation to the Binomial

3.5.3 Normal Approximation to the Binomial

3.5.4 Normal Approximation to the Poisson

3.6 Chebyshev's Theorem

3.7 Empirical Rule

3.8 The Central Limit Theorem

Chapter 4 Sampling Distributions

4.1 Properties of Sample Mean and Variance.

4.2 Population and Sampling Distributions

4.2.1 Population Distribution

4.2.2 Sampling Distribution

4.3 Sampling and Nonsampling Errors

4.4 Mean and Standard Deviation of x

4.5 Shape of the Sampling Distribution of x

4.5.1 Sampling from a Normally Distributed Population

4.5.2 Sampling from a Population that is not Normally Distributed

4.6 Applications of the Sampling Distribution of x

4.7 Population and Sample Proportions

4.8 Sampling Distribution of p

4.9 Mean and Standard Deviation of p

4.10 The Chi-Square Distribution

4.11 The t-Distribution

4.12 The F-Distribution

4.13 Summary

Chapter 5 Estimation

5.1 Point Estimation

5.2 Interval Estimation

5.3 Confidence Interval on Mean, Variance Known

5.4 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown

5.5 Confidence Interval on the Variance of a Normal Distribution

5.6 Confidence Interval on a Population Proportion

5.7 Confidence Interval on the Difference in Two Means, Variance Known

5.8 Confidence Interval on the Difference in Means of Two Normal Distributions, Variances Unknown

5.9 Confidence Interval on μ1 - μ2 for Paired Observations

5.10 Confidence Interval on the Ratio of Variance of Two Normal Distributions

5.11 Confidence Interval on the Difference in Two Proportions

5.12 Sample Size Selection

5.12.1 Sample Size Selection for Estimating Population Mean

5.12.2 Sample Size for the Estimation of Proportion

5.13 Summary

Chapter 6 Hypothesis Testing

6.1 Null Hypothesis and Alternative Hypothesis

6.2 The Critical Region

6.3 Types of Sampling Errors (Type I and Type II Errors).

6.4 Level of Significance

6.5 Tails of a Test

6.6 Hypothesis Test on the Population Mean, Standard Deviation Known

6.7 Hypothesis Test on the Population Mean, Standard Deviation Unknown

6.8 Hypothesis Test for a Population Variance

6.9 Hypothesis Test on a Population Proportion

6.10 Hypothesis Test on Equality of Two Means, Variances Known

6.11 Hypothesis Test on the Means of Two Normal Distributions, Variances Unknown

6.11.1 Case 1:

6.11.2 Case 2:

6.12 Hypothesis Test to Compare Two Population Means (Paired t-Test)

6.13 Hypothesis Test on the Equality of Two Variances

6.14 Hypothesis Test on Two Proportions

6.15 Summary

Chapter 7 Curve Fitting, Regression and Correlation

7.1 Linear Equation

7.2 Curve Fitting With a Linear Equation

7.3 Criteria for a "Best" Fit

7.4 Linear Least-Squares Regression

7.5 Linear Regression Analysis

7.6 Interpretation of a and b

7.7 Standard Deviation of Random Errors

7.8 Coefficient of Determination

7.9 Sampling Distribution of b

7.10 Hypothesis Testing About B

7.11 Linear Correlation

7.12 Estimating the Mean Value of y

7.13 Estimating a Particular Value of y

7.14 Linearization of Non-Linear Relationships

7.15 Polynomial Regression

7.16 Quantification of Error of Linear Regression

7.17 Multiple Linear Regression

7.18 Weighted Least-Squares Method

7.19 Orthogonal Polynomials and Least-Squares Approximation

7.20 Least-Squares Method for Continuous Data

7.21 Approximation Using Orthogonal Polynomials

7.22 Gram-Schmidt Orthogonalization Process

7.23 Additional Example Problems and Solutions

7.24 Summary

Chapter 8 chi-square Tests.

8.1 Introduction

8.2 A Goodness-of-Fit Test

8.3 Contingency Table

8.4 A Test of Independence or Homogeneity

8.5 Inferences about the Population Variance

8.6 Estimation of the Population Variance

8.7 Hypothesis Tests about the Population Variance

Chapter 9 Analysis of Variance

9.1 Introduction

9.2 One-Way Analysis of Variance

9.3 Test Statistic

9.4 One-Way Anova Test

Appendices

Appendix-A Values for n Factorial

Appendix-B Binomial Coefficients

Appendix-C Table of Binomial Probabilities

Appendix-D Cumulative Poisson Distributions

Appendix-E Cumulative Standard Normal Distribution

Appendix-F chi-square Distribution Table

Appendix-G The t-Distribution Table

Appendix-H The F-Distribution Table

Appendix-I Cramer's Rule

Bibliography

Glossary of Technical Terms

Glossary of Symbols

Key Formulae

Answers to Selected Problems.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on online resource; title from PDF title page (ebrary, viewed September 8, 2015).

ISBN:

1-78183-047-9

OCLC:

919481099