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Schaum's Outline of Probability, Random Variables, and Random Processes, Fourth Edition
1 online resource (434 pages) : illustrations.
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 -- 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 -- 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 -- 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 -- 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 -- 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-Lo?ve Expansions -- 6.7 Fourier Transform of Random Processes -- 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 -- CHAPTER 8 Decision Theory -- 8.1 Introduction -- 8.2 Hypothesis Testing -- 8.3 Decision Tests -- 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 -- 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 -- APPENDIX A Normal Distribution -- APPENDIX B Fourier Transform -- B.1 Continuous-Time Fourier Transform -- B.2 Discrete-Time Fourier Transform -- INDEX.
Electronic reproduction. New York, N.Y. : McGraw Hill, 2020. Mode of access: World Wide Web. System requirements: Web browser. Access may be restricted to users at subscribing institutions.
Mode of access: Internet via World Wide Web.
Includes bibliographical references and index.
New York, N.Y. : McGraw-Hill Education, [2020].