DISCRETE STOCHASTIC PROCESSES-2BR.G.Gallager

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1、DISCRETESTOCHASTICPROCESSESDraftof2ndEditionR.G.GallagerAugust17,2009iContents1INTRODUCTIONANDREVIEWOFPROBABILITY11.1Probabilitymodels................................11.1.1Thesamplespaceofaprobabilitymodel................31.1.2Assigningprobabilitiesfor

2、finitesamplespaces............41.2Theaxiomsofprobabilitytheory........................51.2.1Axiomsfortheclassofeventsforasamplespace≠:.........61.2.2Axiomsofprobability..........................71.3Probabilityreview................................81.3.1

3、Conditionalprobabilitiesandstatisticalindependence........81.3.2Repeatedidealizedexperiments.....................101.3.3Randomvariables............................111.3.4Multiplerandomvariablesandconditionalprobabilities.......121.3.5Stochasticprocesse

4、s...........................141.3.6Expectations...............................161.3.7Randomvariablesasfunctionsofotherrandomvariables......191.3.8Conditionalexpectations........................221.3.9Indicatorrandomvariables.......................241.3

5、.10Transforms................................241.4Thelawsoflargenumbers............................251.4.1Basicinequalities.............................261.4.2Weaklawoflargenumberswithafinitevariance...........281.4.3Relativefrequency...................

6、.........301.4.4Thecentrallimittheorem........................31iiCONTENTSiii1.4.5Weaklawwithaninfinitevariance...................331.4.6Stronglawoflargenumbers(SLLN)..................341.4.7Convergenceofrandomvariables....................381.5Relationo

7、fprobabilitymodelstotherealworld................421.5.1Relativefrequenciesinaprobabilitymodel..............421.5.2Relativefrequenciesintherealworld..................431.5.3Statisticalindependenceofreal-worldexperiments.........451.5.4Limitationsofrelat

8、ivefrequencies...................461.5.5Subjectiveprobability..........................471.6Summary.....................................471.7Appendix.....................................491.7.1Tableofstandardrandomvariables.............