Probability Theory
نویسنده
چکیده
4 The Lebesgue integral and expectation 14 4.1 The Lebesgue integral and convergence theorems . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Probability measures and modes of convergence . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Uniform integrability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4 Jensen’s inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.5 Weak law of large numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.6 Types of distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.7 The characteristic function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.8 Normal distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.9 Gaussian processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
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