introduction to probability - dimitri bertsekas and john n tsitsiklis

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1、LECTURENOTESCourse6.041-6.431M.I.T.FALL2000IntroductiontoProbabilityDimitriP.BertsekasandJohnN.TsitsiklisProfessorsofElectricalEngineeringandComputerScienceMassachusettsInstituteofTechnologyCambridge,MassachusettsThesenotesarecopyright-protectedbutmaybefreelydistributedforinstr

2、uctionalnonprofitpruposes.Contents1.SampleSpaceandProbability................1.1.Sets..............................1.2.ProbabilisticModels.......................1.3.ConditionalProbability.....................1.4.Independence..........................1.5.TotalProbabilityTheoreman

3、dBayes’Rule............1.6.Counting...........................1.7.SummaryandDiscussion....................2.DiscreteRandomVariables.................2.1.BasicConcepts.........................2.2.ProbabilityMassFunctions...................2.3.FunctionsofRandomVariables...........

4、.......2.4.Expectation,Mean,andVariance.................2.5.JointPMFsofMultipleRandomVariables.............2.6.Conditioning..........................2.7.Independence..........................2.8.SummaryandDiscussion....................3.GeneralRandomVariables.................3.

5、1.ContinuousRandomVariablesandPDFs.............3.2.CumulativeDistributionFunctions................3.3.NormalRandomVariables....................3.4.ConditioningonanEvent....................3.5.MultipleContinuousRandomVariables..............3.6.DerivedDistributions...............

6、.......3.7.SummaryandDiscussion....................4.FurtherTopicsonRandomVariablesandExpectations......4.1.Transforms...........................4.2.SumsofIndependentRandomVariables-Convolutions.......iiiivContents4.3.ConditionalExpectationasaRandomVariable...........4.4.Sumofa

7、RandomNumberofIndependentRandomVariables....4.5.CovarianceandCorrelation...................4.6.LeastSquaresEstimation....................4.7.TheBivariateNormalDistribution................5.TheBernoulliandPoissonProcesses..............5.1.TheBernoulliProcess.....................

8、.5.2.ThePoissonProcess.......................6.MarkovC