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Contents 9 Preface 5 Chapter 1 Basis of probability 13 1.1 Random ovcnts 13 1.1.1 Random experiments 14 1.1.3 Calculation among random evcnts 18 1.1.4 σ-algebras 22 1.2 Probability 24 1.2.1 What is probability 24 1.2.2 Properties of probability 26 1.2.3 Two fundamental probability models 28 1.2.4 Conditional probability and three important formulas 31 1.2.5 Independence of events 35 1.3 Random variables 37 1.3.1 Definition 37 1.3.2 Cumulative distribution functions 39 1.3.4 Multiple-dimensional random variablcs 46 1.3.5 Distributions of functions of random variables 50 1.3.6 Conditional distributions and indepenclences 56 1.3.7 0rder statistics 59 1.4 Numerical characteristics 62 1.4.1 Definition of mathematical expectations 62 1.4.2 Properties 68 1.4.3 0ther numerical characteristics of random variables 69 1.4.4 Conditional mathematical expectations 85 1.5 Limiting thcoroms 88 1.5.1 Convcrgencc of random variablcs 88 1.5.2 Law of large numbers 92 1.5.3 Central limit thcorcms 96 Exercise 1 98 Answcrs or tips for Excrcisc 1 100 Chapter 2 Stochastic processes 107 2.1 Definition and classification 107 2.1.1 Definition 108 2.1.3 Examples 111 2.2 Statistical laws of stochastic processes

Author

CNKI

Language

EN