概率理论和问题纲要schaums-outline of theory and problems of probability

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1、CONTENTSPageChapterISETTHEORY......................................................1Introduction.Sets,elements.Setoperations.Finiteandcountablesets.Productsets.Classesofsets.Chapter2TECHNIQUESOFCOUNTING....................................16Introduction.Fundamentalprincipleofcoun

2、ting.Factorialnotation.Permutations.Permutationswithrepetitions.Orderedsamples.Binomialcoefficientsandtheorem.Combinations.Orderedpartitions.Treediagrams.Chapter3INTRODUCTIONTOPROBABILITY..............................38Introduction.Samplespaceandevents.Axiomsofprobability.Finite

3、probabilityspaces.Finiteequiprobablespaces.Infinitesamplespaces.Chapter4CONDITIONALPROBABILITYANDINDEPENDENCE..........54Conditionalprobability.Multiplicationtheoremforconditionalprobability.Finitestochasticprocessesandtreediagrams.PartitionsandBayedtheorem.Inde-pendence.Indepen

4、dentorrepeatedtrials.Chapter5RANDOMVARIABLES............................................74Introduction.Distributionandexpectationofafiniterandomvariable.Varianceandstandarddeviation.Jointdistribution.Independentrandomvariables.Func-tionsofarandomvariable.Discreterandomvariablesi

5、ngeneral.Continuousrandomvariables.Cumulativedistributionfunction.Tchebycheff’sinequality.Lawoflargenumbers..Chapter6BINOMIAL,NORMALANDPOISSONDISTRIBUTIONS..........105Binomialdistribution.Normaldistribution.Normalapproximationtothebinomialdistribution.Centrallimittheorem.Poisso

6、ndistribution.Multinomialdistribution.Chapter7MARKOVCHAINS................................................126Introduction.Probabilityvectors,stochasticmatrices.Regularstochasticmatrices.Fixedpointsandregularstochasticmatrices.Markovchains.Highertransitionprobabilities.Stationary

7、distributionofregularMarkovchains.Absorbingstates.~INDEX...........................................................................152ChapterISetTheoryINTRODUCTIONThischaptertreatssomeoftheelementaryideasandconceptsofsettheorywhicharenecessaryforamodernintroductiontoprobabilityt

8、heory.SETS,ELEMENTSAnywelldefinedlistorcollecti