Probability, Statistics and Random Processes

✍ Scribed by Pappu Kousalya

• Publisher: Pearson Education
• Year: 2013
• Tongue: English
• Leaves: 593
• Category: Library

✦ Table of Contents

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