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Chapter 4. Functions of Random Variables, Expectation, Limit Theorems 122
4.1 Introduction 122
4.2 Functions of One Random Variable 122
4.3 Functions of Two Random Variables 123
4.4 Functions of n Random Variables 124
4.5 Expectation 125
4.6 Moment Generating Functions 126
4.7 Characteristic Functions 127
4.8 The Laws of Large Numbers and the Central Limit Theorem 128
Solved Problems 129
Chapter 5. Random Processes 161
5.1 Introduction 161
5.2 Random Processes 161
5.3 Characterization of Random Processes 161
5.4 Classification of Random Processes 162
5.5 Discrete-Parameter Markov Chains 165
5.6 Poisson Processes 169
5.7 Wiener Processes 172
Solved Problems 172
Chapter 6. Analysis and Processing of Random Processes 209
6.1 Introduction 209
6.2 Continuity, Differentiation, Integration 209
6.3 Power Spectral Densities 210
6.4 White Noise 213
6.5 Response of Linear Systems to Random Inputs 213
6.6 Fourier Series and Karhunen-Loéve Expansions 216
6.7 Fourier Transform of Random Processes 218
Solved Problems 219
Chapter 7. Estimation Theory 247
7.1 Introduction 247
7.2 Parameter Estimation 247
7.3 Properties of Point Estimators 247
7.4 Maximum-Likelihood Estimation 248
7.5 Bayes' Estimation 248
7.6 Mean Square Estimation 249
7.7 Linear Mean Square Estimation 249
Solved Problems 250
