Book description
Probability, Statistics and Random Processes is designed to meet the requirements of students and is intended for beginners to help them understand the concepts from the first principles. Spread across 16 chapters, it discusses the theoretical aspects that have been refined and updated to reflect the current developments in the subjects. It expounds on theoretical concepts that have immense practical applications, giving adequate proofs to establish significant theorems.Table of contents
 Cover
 Title Page
 Contents
 Preface

Chapter 1: Probability
 Introduction
 1.1 Elementary Concepts of Set Theory
 1.2 Permutations and Combinations
 1.3 Introduction of Probability
 1.4 Axioms of Probability
 1.5 Some Elementary Results
 1.6 Conditional Probability
 1.7 Theorem of Total Probability
 1.8 Baye’s Theorem
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions

Chapter 2: Random Variables (Discrete and Continuous)
 Introduction
 2.1 Random Variable
 2.2 Probability Mass Function (PMF)
 2.3 Probability Density Function (PDF)
 2.4 Joint Probability Distributions
 2.5 Joint Density Function F(X, Y)
 2.6 Stochastic Independence
 2.7 Transformation of OneDimensional Random Variable
 2.8 Transformation of TwoDimensional Random Variable
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions

Chapter 3: Mathematical Expectation
 Introduction
 3.1 Mathematical Expectation
 3.2 Variance
 3.3 Expectation of a Function of Random Variables
 3.4 Variance for Joint Distributions
 3.5 Covariance
 3.6 Conditional Expectation
 3.7 Chebychev’s Inequality
 3.8 Moments
 3.9 Moment Generating Function
 3.10 Characteristic Function
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions
 Chapter 4: Standard Discrete Distributions
 Chapter 5: Standard Continuous Distributions

Chapter 6: Sampling Theory and Distribution
 Introduction
 6.1 Some Definitions
 6.2 Types of Sampling
 6.3 Advantages of Sampling
 6.4 Sampling Distribution of a Statistic
 6.5 Standard Error
 6.6 Importance of Standard Error
 6.7 Sampling from Normal and NonNormal Populations
 6.8 Finite Population Correction (FPC) Factor
 6.9 Sampling Distribution of Means
 6.10 When Population Variance is Unknown
 6.11 Sampling Distribution of the Difference between Two Means
 6.12 Sampling Distribution of Variance
 6.13 The ChiSquare Distribution
 6.14 The Student’s tDistribution
 6.15 FDistribution
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions
 Chapter 7: Testing of Hypothesis (Large Samples)

Chapter 8: Test of Hypothesis (Small Samples)
 Introduction
 8.1 Student’s tDistribution
 8.2 Critical Values of t
 8.3 tTest for Single Mean
 8.4 tTest for Difference of Means
 8.5 Paired tTest for Difference of Means
 8.6 Snedecor’s FDistribution
 8.7 ChiSquare Distribution
 8.8 Test for Independence of Attributes
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions

Chapter 9: Estimation
 Introduction
 9.1 Point Estimation
 9.2 Characteristics of Estimators
 9.3 Interval Estimation
 9.4 Confidence Interval
 9.5 Some Results
 9.6 Confidence Interval for Difference between Two Means (Known Variances)
 9.7 Confidence Interval for Difference between Two Means (Unknown Variances)
 9.8 Confidence Interval for Difference of Means (Unknown and Unequal Variances)
 9.9 Confidence Interval for Difference between Means for Paired observations
 9.10 Confidence Interval for Estimating the Variance
 9.11 Confidence Interval for Estimating the Ratio of Two Variances
 9.12 Bayesian Estimation
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions
 Chapter 10: Curve Fitting

Chapter 11: Correlation
 Introduction
 11.1 Types of Correlation
 11.2 Methods of Correlation
 11.3 Properties of Correlation Coefficient
 11.4 Coefficient of Correlation for Grouped Data
 11.5 Rank Correlation
 11.6 Limitations of Spearman’s Correlation Coefficient Method
 11.7 Tied Ranks
 11.8 Concurrent Deviations Method
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions

Chapter 12: Regression
 12.1 Regression
 12.2 Lines of Regression
 12.3 Regression Coefficients
 12.4 Difference between Regression and Correlation Analysis
 12.5 Angle between Two Lines of Regression
 12.6 Standard Error of Estimate
 12.7 Limitations of Regression Analysis
 12.8 Regression Curves
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions

Chapter 13: Queuing Theory
 Introduction
 13.1 Elements of a Queuing Model
 13.2 Distribution of InterArrival Time
 13.3 Distribution of Service Time
 13.4 Queuing Process
 13.5 Transient State and Steady State
 13.6 Some Notations
 13.7 Probability Distributions in Queuing System
 13.8 Pure Birth Process
 13.9 Pure Death Process
 13.10 Classification of Queuing Models: (Single Server Queuing Models)
 13.11 MultiServer Queuing Models
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions

Chapter 14: Design of Experiments
 Introduction
 14.1 Assumptions of Analysis of Variance
 14.2 OneWay Classification
 14.3 The Analysis from Decomposition of the Individual Observations
 14.4 TwoWay Classification
 14.5 Completely Randomized Design (CRD)
 14.6 Latin Square Design (LSD)
 14.7 Randomized Block Design (RBD)
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions

Chapter 15: Random Process
 Introduction
 15.1 Classification of Random Processes
 15.2 Stationarity
 15.3 Second Order Stationary Process
 15.4 Wide Sense Stationary Process
 15.5 Cross Correlation Function
 15.6 Statistical Averages
 15.7 Time Averages
 15.8 Statistical Independence
 15.9 Ergodic Random Process
 15.10 MeanErgodic Theorem
 15.11 Correlation Ergodic Process
 15.12 Correlation Functions
 15.13 Covariance Functions
 15.14 Spectral Representation
 15.15 Discrete Time Processes
 15.16 Discrete Time Sequences
 15.17 Some Noise Definitions
 15.18 Types of Noise
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions

Chapter 16: Advanced Random Process
 Introduction
 16.1 Poisson Process
 16.2 Mean and Auto Correlation of the Poisson Process
 16.3 Markov Process
 16.4 ChapmanKolmogorov Theorem
 16.5 Definitions in Markov Chain
 16.6 Application to the Theory of Queues
 16.7 Random Walk
 16.8 Gaussian Process
 16.9 Band Pass Process
 16.10 Narrow Band Gaussian Process
 16.11 Band Limited Process
 Definitions at a Glance
 Formulae at a Glance
 Objective Type Questions
 Appendix A
 Appendix B
 Appendix C
 Appendix D
 Notes
 Acknowledgements
 Copyright
 Back Cover
Product information
 Title: Probability, Statistics and Random Processes
 Author(s):
 Release date: February 2013
 Publisher(s): Pearson India
 ISBN: 9789332513914
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