Probability, Statistics and Random Processes

Cover
Contents
Preface
Acknowledgements
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 One-Dimensional Random Variable
	2.8 Transformation of Two-Dimensional 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
	Introduction
	4.1 Binomial Distribution
	4.2 Poisson Distribution
	4.3 Negative Binomial Distribution
	4.4 Geometric Distribution
	4.5 Hyper Geometric Distribution
	4.6 Uniform Distribution
		Definitions at a Glance
		Formulae at a Glance
		Objective Type Questions
Chapter 5:
Standard Continuous Distributions
	Introduction
	5.1 Normal Distribution
	5.2 Exponential Distribution
	5.3 Gamma Distribution
	5.4 Weibull Distribution
	5.5 Central Limit Theorem
		Definitions at a Glance
		Formulae at a Glance
		Objective Type Questions
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 Non-Normal 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 Chi-Square Distribution
	6.14 The Student’s t-Distribution
	6.15 F-Distribution
		Definitions at a Glance
		Formulae at a Glance
		Objective Type Questions
Chapter 7:
Testing of Hypothesis (Large Samples)
	Introduction
	7.1 Statistical Hypothesis
	7.2 Tests of Significance
	7.3 Some Important Definitions
	7.4 Steps Involved in Testing of Hypothesis
	7.5 Tests of Significance
		Definitions at a Glance
		Formulae at a Glance
		Objective Type Questions
Chapter 8:
Test of Hypothesis (Small Samples)
	Introduction
	8.1 Student’s t-Distribution
	8.2 Critical Values of t
	8.3 t-Test for Single Mean
	8.4 t-Test for Difference of Means
	8.5 Paired t-Test for Difference of Means
	8.6 Snedecor’s F-Distribution
	8.7 Chi-Square 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
	Introduction
	10.1 The Method of Least Squares
	10.2 Fitting of a Straight Line
	10.3 Fitting of a Second Degree Parabola
	10.4 Fitting of Exponential Curve and Power Curve
		Definitions at a Glance
		Formulae at a Glance
		Objective Type Questions
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 Inter-Arrival 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 Multi-Server 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 One-Way Classification
	14.3 The Analysis from Decomposition of the Individual Observations
	14.4 Two-Way 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 Mean-Ergodic 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 Chapman-Kolmogorov 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
Index