# Probability and Statistics for Engineers, As per AICTE

ISBN: 9788126512348

612 pages

## Description

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 would be equally helpful for six sigma practitioners in industries. 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 requirements of engineering students, the text covers all important topics, emphasizing basic engineering and science applications.

1. Probability Concepts

1.1 Introduction

1.2 Important Definitions

1.3 Approaches of Measuring Probability

1.4 Bayes’ Theorem

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

3. Expectation and Moment-Generating Function

3.1 Introduction

3.2 Definition and Properties of Expectation

3.3 Moments and Moment-Generating Function

4. Standard Discrete Distribution Functions

4.1 Introduction

4.2 Discrete Distributions

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

5.4 Gamma Random Variable and Its Distribution

5.5 Normal Random Variable and Its Distribution

6. Chebyshev’s Inequality and Central Limit Theorem

6.1 Introduction

6.2 Chebyshev’s Theorem (or Inequality)

6.3 Asymptotic Properties of Random Sequences

6.4 Central Limit Theorem

7. Two-Dimensional Random Variables

7.1 Introduction

7.2 Discrete Case: Joint Probability Mass Function

7.3 Continuous Case: Joint Probability Density Function

7.4 Stochastic Independence of Random Variables

7.5 Expectation of Two-Dimensional Random Variables

7.6 Conditional Mean and Conditional Variance

8. Transformation of Random Variables

8.1 Introduction

8.2 One-Dimensional Random Variable

8.3 Two-Dimensional Random Variables

9. Point Estimation and Minimum Risk Estimator

9.1 Introduction

9.2 Types of Estimation

10. Sampling Distributions and Interval Estimation

10.1 Introduction

10.2 Sampling Distributions

10.3 Interval Estimation

11. Testing of Hypotheses

11.1 Introduction

11.2 Testing of Hypothesis

11.3 Classification of Hypothesis Tests

11.4 Large Sample Tests

11.5 Small Sample Tests

12. Simple Correlation and Regression

12.1 Introduction to Simple Correlation

12.2 Properties of Correlation Coefficient

12.3 Rank Correlation Coefficient

12.4 Introduction to Simple Regression

13. Analysis of Variance: One-Way and Two-Way Analyses

13.1 Introduction

13.2 Single-Factor (One-Way ANOVA) Experiment and Linear Statistical Model

13.3 Fixed Effects Model and ANOVA

13.4 Random Effects Model and ANOVA

13.5 Computations for Sum of Squares

13.6 Multiple Comparison Test: Grouping of Means

13.7 Single-Factor (Two-Way ANOVA) Experiment and Linear Statistical Model (Completely Randomized Block Design)

13.8 Fixed Effects Model for Two-Way ANOVA

13.9 Random Effects Model for Two-Way ANOVA

13.10 Computations for Sum of Squares

14. Latin Square Design and Two-Factor Factorial Design

14.1 Introduction

14.2 Latin Square Design

14.3 Two-Factor Factorial Experiment

15. Statistical Quality Control and Six Sigma Metrics

15.1 Introduction

15.2 Statistical Quality Control

15.3 Control Charts for Variables

15.4 Control Charts for Attributes

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

15.6 Process Capability and Process Capability Index

15.7 Six Sigma

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 Construction of Various Control Charts

Appendix G Least Significant Studentized Ranges

Answers

Index