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Probability and Statistics

Book Description

This book is designed for engineering students studying for the core paper on probability and statistics. The topics have been dealt in a coherent manner, supported by illustrations for better compre¬hension. Each chapter is replete with examples and exercises. The book also has numerous Multiple Choice Questions at the end of each chapter, thus providing the student with an abundant repository of exam specific problems.

Table of Contents

  1. Title Page
  2. Roadmap to the Syllabus
  3. Contents
  4. Preface
  5. About the Author
  6. List of Symbols
  7. 1. Probability
    1. 1.1 Introduction
    2. 1.2 Sets and Set Operations
    3. 1.3 Principle of Counting
    4. 1.4 Permutations and Combinations
    5. 1.5 Binomial Expansion
    6. 1.6 Introduction to Probability
    7. 1.7 Axioms of Probability
    8. 1.8 Basic Theorems
    9. 1.9 Conditional Probability and Independent Events
    10. 1.10 Theorem of Total Probability (or the Rule of Elimination)1-20
    11. 1.11 Bayes’ Theorem or Rule
    12. Exercises
    13. Multiple Choice Questions
    14. Fill in the Blanks
  8. 2. Probability Distribution
    1. 2.1 Introduction
    2. 2.2 Random Variables
    3. 2.3 Probability Distribution
    4. 2.4 Expectation or Mean or Expected Value
    5. 2.5 Variance and Standard Deviation
    6. 2.6 Probability Density Functions
    7. 2.7 Chebyshev’s Theorem
    8. Exercises
    9. Fill in the Blanks
  9. 3. Special Distribution
    1. 3.1 Introduction
    2. 3.2 Binomial (Bernoulli) Distribution
    3. 3.3 Poisson Distribution
    4. 3.4 Uniform Distribution
    5. 3.5 Exponential Distribution
    6. 3.6 Normal Distribution
    7. Exercises
    8. Multiple Choice Questions
    9. Fill in the Blanks
  10. 4. Sampling Distributions
    1. 4.1 Introduction
    2. 4.2 Population and Sample
    3. 4.3 Sampling Distribution
    4. 4.4 Sampling Distribution of Means (σ Known)4-3
    5. 4.5 Sampling Distribution of ­Proportions
    6. 4.6 Sampling Distribution of Differences and Sums
    7. 4.7 Sampling Distribution of Means (σ Unknown): t-Distribution
    8. 4.8 Chi-square (χ2) Distribution
    9. 4.9 Sampling Distribution of Variance σ 24-20
    10. 4.10 Snedecor’s F-Distribution
    11. 4.11 Fisher’s z-Distribution
    12. Exercises
    13. Multiple Choice Questions
    14. Fill in the Blanks
  11. 5. Estimation Theory
    1. 5.1 Introduction
    2. 5.2 Statistical Inference
    3. 5.3 Point Estimation
    4. 5.4 Interval Estimation
    5. 5.5 Bayesian Estimation
    6. Exercises
    7. Fill in the Blanks
  12. 6. Inferences Concerning Means and Proportions
    1. 6.1 Introduction
    2. 6.2 Statistical Hypotheses
    3. 6.3 Tests of Hypotheses and ­Significance
    4. 6.4 Type I and Type II Errors
    5. 6.5 Levels of Significance
    6. 6.6 Statistical Test of Hypothesis Procedure
    7. 6.7 Reasoning of Statistical Test of Hypothesis
    8. 6.8 Inference Concerning Two Means
    9. Exercises
    10. Fill in the Blanks
  13. 7. Tests of Significance
    1. 7.1 Introduction
    2. 7.2 Test for One Mean (Small Sample)7-1
    3. 7.3 Test for Two Means
    4. 7.4 Test of Hypothesis
    5. 7.5 Analysis of r × c Tables (Contingency Tables)7-18
    6. 7.6 Goodness-of-Fit Test: χ2 ­Distribution
    7. 7.7 Estimation of Proportions
    8. Exercises
    9. Fill in the Blanks
  14. 8. Curve Fitting: Regression and Correlation Analysis
    1. 8.1 Introduction
    2. 8.2 Linear Regression
    3. 8.3 Regression Analysis
    4. 8.4 Inferences Based on Least Squares Estimation
    5. 8.5 Multiple Regression
    6. 8.6 Correlation Analysis
    7. 8.7 Least Squares Line in Terms of Sample Variances and Covariance
    8. 8.8 Standard Error of Estimate
    9. 8.9 Spearman’s Rank Correlation
    10. 8.10 Correlation for Bivariate Frequency Distribution
    11. Exercises
    12. Fill in the Blanks
  15. 9. Analysis of Variance
    1. 9.1 Analysis of Variance (ANOVA)
    2. 9.2 What is ANOVA?
    3. 9.3 The Basic Principle of ANOVA
    4. 9.4 ANOVA Technique
    5. 9.5 Setting Up Analysis of Variance Table
    6. 9.6 Shortcut Method for One-Way ANOVA
    7. 9.7 Coding Method
    8. 9.8 Two-Way ANOVA
    9. 9.9 ANOVA in Latin-Square Design
    10. Exercises
  16. 10. Statistical Quality Control
    1. 10.1 Properties of Control Charts
    2. 10.2 Shewhart Control Charts for Measurements
    3. 10.3 Shewhart Control Charts for Attributes
    4. 10.4 Tolerance Limits
    5. 10.5 Acceptance Sampling
    6. 10.6 Two-stage Acceptance Sampling
  17. 11. Queueing Theory
    1. 11.1 Introduction
    2. 11.2 Queues or Waiting Lines
    3. 11.3 Elements of a Basic Queueing System
    4. 11.4 Description of a Queueing System
    5. 11.5 Classification of Queueing Systems
    6. 11.6 Queueing Problem
    7. 11.7 States of Queueing Theory
    8. 11.8 Probability Distribution in Queueing Systems
    9. 11.9 Kendall’s Notation for Representing Queueing Models
    10. 11.10 Basic Probabilistic Queueing Models
    11. Exercises
    12. Fill in the Blanks
  18. Appendix A
  19. Appendix B
  20. Appendix C
  21. Additional Solved Problems