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

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