Probability, Random Variables, And Random Processes

✍ Scribed by Hwei P. Hsu

• Publisher: McGraw Hill
• Year: 2019
• Tongue: English
• Leaves: 434
• Series: Schaum's Outlines
• Edition: 4
• Category: Library

✦ Table of Contents

Cover
Title Page
Copyright Page
Preface to The Second Edition
Preface to The First Edition
Contents
CHAPTER 1 Probability
1.1 Introduction
1.2 Sample Space and Events
1.3 Algebra of Sets
1.4 Probability Space
1.5 Equally Likely Events
1.6 Conditional Probability
1.7 Total Probability
1.8 Independent Events
Solved Problems
CHAPTER 2 Random Variables
2.1 Introduction
2.2 Random Variables
2.3 Distribution Functions
2.4 Discrete Random Variables and Probability Mass Functions
2.5 Continuous Random Variables and Probability Density Functions
2.6 Mean and Variance
2.7 Some Special Distributions
2.8 Conditional Distributions
Solved Problems
CHAPTER 3 Multiple Random Variables
3.1 Introduction
3.2 Bivariate Random Variables
3.3 Joint Distribution Functions
3.4 Discrete Random Variables—Joint Probability Mass Functions
3.5 Continuous Random Variables—Joint Probability Density Functions
3.6 Conditional Distributions
3.7 Covariance and Correlation Coefficient
3.8 Conditional Means and Conditional Variances
3.9 N-Variate Random Variables
3.10 Special Distributions
Solved Problems
CHAPTER 4 Functions of Random Variables, Expectation, Limit Theorems
4.1 Introduction
4.2 Functions of One Random Variable
4.3 Functions of Two Random Variables
4.4 Functions of n Random Variables
4.5 Expectation
4.6 Probability Generating Functions
4.7 Moment Generating Functions
4.8 Characteristic Functions
4.9 The Laws of Large Numbers and the Central Limit Theorem
Solved Problems
CHAPTER 5 Random Processes
5.1 Introduction
5.2 Random Processes
5.3 Characterization of Random Processes
5.4 Classification of Random Processes
5.5 Discrete-Parameter Markov Chains
5.6 Poisson Processes
5.7 Wiener Processes
5.8 Martingales
Solved Problems
CHAPTER 6 Analysis and Processing of Random Processes
6.1 Introduction
6.2 Continuity, Differentiation, Integration
6.3 Power Spectral Densities
6.4 White Noise
6.5 Response of Linear Systems to Random Inputs
6.6 Fourier Series and Karhunen-Loéve Expansions
6.7 Fourier Transform of Random Processes
Solved Problems
CHAPTER 7 Estimation Theory
7.1 Introduction
7.2 Parameter Estimation
7.3 Properties of Point Estimators
7.4 Maximum-Likelihood Estimation
7.5 Bayes’ Estimation
7.6 Mean Square Estimation
7.7 Linear Mean Square Estimation
Solved Problems
CHAPTER 8 Decision Theory
8.1 Introduction
8.2 Hypothesis Testing
8.3 Decision Tests
Solved Problems
CHAPTER 9 Queueing Theory
9.1 Introduction
9.2 Queueing Systems
9.3 Birth-Death Process
9.4 The M/M/1 Queueing System
9.5 The M/M/s Queueing System
9.6 The M/M/1/K Queueing System
9.7 The M/M/s/K Queueing System
Solved Problems
CHAPTER 10 Information Theory
10.1 Introduction
10.2 Measure of Information
10.3 Discrete Memoryless Channels
10.4 Mutual Information
10.5 Channel Capacity
10.6 Continuous Channel
10.7 Additive White Gaussian Noise Channel
10.8 Source Coding
10.9 Entropy Coding
Solved Problems
APPENDIX A Normal Distribution
APPENDIX B Fourier Transform
B.1 Continuous-Time Fourier Transform
B.2 Discrete-Time Fourier Transform
INDEX