Schaum's Outline of Probability, Random Variables, and Random Processes, Fourth Edition

Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entitlements included with the product. Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately, there’s Schaum’s. More than 40 million students have trusted Schaum’s to help them succeed in the classroom and on exams. Schaum’s is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. Schaum’s Outline of Probability, Random Variables, and Random Processes, Fourth Edition is packed with hundreds of examples, solved problems, and practice exercises to test your skills. This updated guide approaches the subject in a more concise, ordered manner than most standard texts, which are often filled with extraneous material. Schaum’s Outline of Probability, Random Variables, and Random Processes, Fourth Edition features: •  405 fully-solved problems •  22 problem-solving videos •  An accessible review of probability and statistics concepts •  Clear, concise explanations of probability, random variables, and random processes •  Content supplements the major leading textbooks in probability and statistics •  Content that is appropriate for Probability, Random Processes, Stochastic Processes, Probability and Random Variables, Introduction to Probability and Statistics courses PLUS: Access to the revised Schaums.com website and new app, containing 22 problem-solving videos, and more. Schaum’s reinforces the main concepts required in your course and offers hundreds of practice exercises to help you succeed. Use Schaum’s to shorten your study time—and get your best test scores! Schaum’s Outlines—Problem solved.

Table of Contents:
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