Probability and Statistics for Engineers

Probability and Statistics for Engineers

Dr. J. Ravichandran

ISBN: 13:  978-81-265-2350-4

Pages: 608/ Price: Rs 349/-

 About the book

Probability and Statistics for Engineers is written for undergraduate students of engineering and physical sciences. Besides the students of B.E. and B.Tech., those pursuing MCA and MCS can also find the book useful. The book is equally useful to six sigma practitioners in industries.

 A comprehensive yet concise, the text is well-organized in 15 chapters that can be covered in a one-semester course in probability and statistics. Designed to meet the requirement of engineering students, the text covers all important topics, emphasizing basic engineering and science applications.

 Assuming the knowledge of elementary calculus, all solved examples are real-time, well-chosen, self-explanatory and graphically illustrated that help students understand the concepts of each topic. Exercise problems and MCQs are given with answers. This will help students well prepare for their exams.

 Key Features

  • Discusses all important topics in 15 well-organized chapters.
  • Highlights a set of learning goals in the beginning of all chapters.
  • Substantiate all theories with solved examples to understand the topics.
  • Provides vast collections of problems and MCQs based on exam papers.
  • Lists all important formulas and definitions in tables in chapter summaries.
  • Explains Process Capability and Six Sigma metrics coupled with Statistical Quality Control in a full dedicated chapter.
  • Presents all important statistical tables in 7 appendixes.

 Includes excellent pedagogy:

-        177 figures

-        69 tables

-        210 solved examples

-        248 problem with answers

-        164 MCQs with answers

 About the author

DR. J. RAVICHANDRAN, Ph.D., is an associate professor at the Department of Mathematics, Amrita Vishwa Vidhyapeetham, Coimbatore, India. Earlier, he served the Statistical Quality Control department at a manufacturing industry for more than 12 years. His areas of research include statistical quality control, statistical inference, six sigma, total quality management and statistical pattern recognition. A senior member of the American Society for Quality (ASQ) for over 20 years and a member of the Indian Society for Technical Education (ISTE), Dr. Ravichandran has contributed to quality higher education by organizing a national-level conference on Quality Improvement Concepts and Their Implementation in higher education and publishing proceedings.

 Table of Contents

Preface

1.            Probability Concepts

1.1          Introduction

1.2          Important Definitions

1.2.1      Random Experiment

1.2.2      Trial

1.2.3      Sample Space

1.2.4      Mutually Exclusive Events

1.2.5      Independent Events

1.2.6      Dependent Events

1.2.7      Equally Likely Events

1.2.8      Exhaustive Events

1.3          Approaches of Measuring Probability

1.3.1      Mathematical (or Classical or Apriori) Probability

1.3.2      Statistical (or Empirical or Posteriori) Probability

1.3.3      Axiomatic Approach to Probability

1.3.4      Law of Addition of Probabilities

1.3.5      Law of Multiplication of Probability and Conditional Probability

1.4          Bayes’ Theorem

Solved Examples

Summary

Problems

Multiple-Choice Questions

 2.            Random Variables and Distribution Functions

2.1          Introduction

2.2          Random Variable

2.3          Discrete Random Variable

2.4          Continuous Random Variable

2.5          Cumulative Distribution Function

Solved Examples

Summary

Problems

Multiple-Choice Questions

 3.            Expectation and Moment-Generating Function

3.1          Introduction

3.2          Definition and Properties of Expectation

3.3          Moments and Moment-Generating Function

3.3.1      Raw and Central Moments

3.3.2      Relationship between Central and Raw Moments

3.3.3      Moments about an Arbitrary Value

3.3.4      Moment-Generating Function

3.3.5      Properties of Moment-Generating Function

3.3.6      Characteristic Function

Solved Examples

Summary

Problems

Multiple-Choice Questions

 4.            Standard Discrete Distribution Functions

4.1          Introduction

4.2          Discrete Distributions

4.2.1      Binomial Random Variable and Its Distribution

4.2.2      Poisson Random Variable and Its Distribution

4.2.3      Geometric Random Variables and Their Distributions:

4.2.4      Uniform Random Variable and Its Distribution

Solved Examples

Summary

Problems

Multiple-Choice Questions

 5.            Some Standard Continuous Distribution Functions

5.1          Introduction

5.2          Uniform Random Variable and Its Distribution

5.3          Exponential Random Variable and its Distribution

5.3.1      Definition 1: If λ is given as a number of occurrences per unit time

5.3.2      Definition 1: If λ is given as time per occurrence

5.3.3      Derivation of Mean and Variance using Moment-Generating Function

5.3.4      Memory-less Property of Exponential Distribution

5.4          Gamma Random Variable and Its Distribution

5.4.1      Definition 1: Gamma Distribution with Two Parameters α and β

5.4.2      Definition 2: Gamma Distribution with One Parameter α

5.4.3      Derivation of Mean and Variance using Moment-Generating Function

5.4.4      Some Particular Cases of Gamma Distribution

5.5          Normal Random Variable and Its Distribution

5.5.1      Mean and Variance

5.5.2      Properties of Normal Distribution

5.5.3      Standard Normal Density and Distribution

5.5.4      Derivation of Mean and Variance using Moment-Generating Function

Solved Examples

Summary

Problems

Multiple-Choice Questions

 6.            Chebyshev’s Theorem and Limit Theorems

6.1          Introduction

6.2          Chebyshev’s Theorem or Chebyshev’s Inequality

6.3          Asymptotic Properties of Random Sequences

6.3.1      Sequence of Random Variables

6.3.2      Convergence Everywhere

6.3.3      Convergence Almost Everywhere

6.3.4      Convergence in Mean Square Sense

6.3.5      Convergence in Probability

6.3.6      Convergence in Distribution

6.3.7      Bernoulli’s Law of Large Numbers

6.4          Central Limit Theorem

6.4.1      Liapounoff’s Form

6.4.2      Lindberg–Levy’s Form

Solved Examples

Summary

Problems

Multiple-Choice Questions

 7.            Two-Dimensional Random Variables

7.1          Introduction

7.2          Discrete Case: Joint Probability Mass Function

7.2.1      Definitions

7.2.2      Marginal Probabilities

7.2.3      Conditional Probabilities

7.2.4      Cumulative Distribution Function of Joint Discrete Random Variables

7.3          Continuous Case: Joint Probability Density Function

7.3.1      Definitions

7.3.2      Marginal Probability Density Functions

7.3.3      Conditional Probability Density Functions

7.3.4      Cumulative Distribution Function of Joint Continuous Random Variables

7.4          Stochastic Independence of Random Variables

7.5          Expectation of Two-Dimensional Random Variables

7.6          Conditional Mean and Conditional Variance

7.6.1      Conditional Mean

7.6.2      Conditional Variance

Solved Examples

Summary

Problems

Multiple-Choice Questions

 8.            Transformation of One- and Two-Dimensional Random Variables

8.1          Introduction

8.2          One-Dimensional Random Variable

8.3          Two-Dimensional Random Variables

Solved Examples

Summary

Problems

Multiple-Choice Questions

 9.            Theory of Estimation: Point Estimation and Minimum Risk Estimator

9.1          Introduction

9.2          Sampling Distributions

9.2.1      Distribution of Sample Means

9.2.2      Distribution of Sample Variances

9.2.3      t-Distribution

9.2.4      Chi-Square Distribution

9.2.5      F-Distribution

9.3          Methods of Estimation

9.3.1      Point Estimation

9.3.2      Properties

9.3.3      Maximum Likelihood Estimation

9.4          Interval Estimation

9.4.1      Mean

9.4.2      Difference of Two Means

9.4.2      Single Proportion

9.4.3      Difference of Two Proportions

9.3.4      Single Variance

9.3.5      Ratio of Two Variances

Solved Examples

Summary

Problems

Multiple-Choice Questions

 10. Theory of Estimation: Sampling Distributions and Interval Estimation

 10.1        Introduction

10.2        Large Sample Tests

10.2.1    Normal Tests for Single Proportion

10.2.2    Normal Test for Difference of Two Proportions

10.2.3    Normal Test for Single Mean

10.2.4    Normal Test for Difference of Two Means

10.3        Small Sample Tests

10.3.1    t-Test for Single Mean

10.3.2    t-Test for Difference of Two Means

10.3.3    Chi-Square Test for Single Variance

10.3.4    F-Test for Ratio of Two Variances

10.3.5    Chi-Square Test for Goodness-of-Fit

10.3.6    Chi-Square Test for Independence of Attributes

11.3.7    Tests for Correlation Coefficient

Solved Examples

Summary

Problems

Multiple-Choice Questions

 11. Simple Correlation and Regression

11.1        Introduction to Simple Correlation

11.1.1    Scatter Plot

11.1.2    Correlation Coefficient

11.2        Properties of Correlation Coefficient

11.3        Rank Correlation Coefficient

11.4        Introduction to Simple Regression

11.4.1    Estimation of Regression Lines

11.4.2    Angle between Two Regression Lines

Solved Examples

Summary

Problems

Multiple-Choice Questions

 12. Analysis of Variance

12.1        Introduction

12.2        One-Way ANOVA

12.3        Two-Way ANOVA

12.4        Randomized Block Designs

12.4        Two-Factorial Designs

Solved Examples

Summary

Problems

Multiple-Choice Questions

 13. Statistical Quality Control

13.1        Introduction

13.2        Control Charts for Attributes

13.2.1    p-Chart

13.2.2    np-Chart

13.3        Control Charts for Variables

13.3.1    X-Bar and R-Charts

13.3.1    Standard Deviation Chart

Solved Examples

Summary

Problems

Multiple-Choice Questions

 14. Exploratory data analysis

14.1        Introduction

14.2        Representation of Data

14.2.1    Tabulation

14.2.2    Graphical Representation

14.2.3    Histogram

14.2.4    Stem-and-Leaf

14.2.4    Box Plot

14.2.5    Normal Probability Plot

Solved Examples

Summary

Problems

Multiple-Choice Questions

 15. Statistical Quality Control and Six Sigma Metrics

15.1        Introduction

15.2        Statistical Quality Control

15.2.1    Relation Between Confidence Limits and Control Limits

15.2.2    Types of Control Charts

15.3        Control Charts for Variables

                15.3.1     -Chart (Control Chart for Means)

                15.3.2    R-Chart (Control Chart for Ranges)

                15.3.3    S-Chart (Control Chart for Standard Deviation)

                15.3.4    X-Chart (Control Charts for Individual Observations)

15.4        Control Charts for Attributes

                15.4.1    p-Chart (Control Chart for Proportion Defectives)

                15.4.2    C-Chart (Control Chart for Number of Defects) and U-Chart (Control Chart for Number Defects per  Unit)

15.5        Out-of-Control Situations in Control Charts and Process Monitoring

15.6        Process Capability and Process Capability Index

15.7        Six Sigma

                15.7.1    Six Sigma Metrics

                15.7.2    Sigma Levels and Process Capabilities

Solved Examples

Summary

Problems

Multiple-Choice Questions

 Appendix A        Other Standard Distributions

Appendix B         Standard Normal Table 

Appendix C         t-Table

Appendix D        Chi-Square Table

Appendix E         F-Table

Appendix F         Duncan’s Test

Appendix G        Control Chart Factors

Answers

Index

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