1 CombinatorialAnalysis 1.1 Introduction 1.2 TheBasicPrincipleofCounting 1.3 Permutations 1.4 Combinations 1.5 MultinomialCoefficients 1.6 TheNumberofIntegerSolutlonsofEquations Summary Problems TheoreticalExercises Self-TestProblemsandExercises 2 AxiomsofProbability 2.1 Introduction 2.2 SampleSpaceandEvents 2.3 AxiomsofProbability 2.4 SomeSimplePropositions 2.5 SampleSpaceHavingEquallyLikelyOutcomes 33 2.6 ProbabilityasaContinuousSetFunction 2.7 ProbabilityasaMeasureofBelief Summary Problems TheoreticalExercises Self-TestProblemsandExercises 3 ConditionalProbabilityandIndependence 3.1 Introduction 3.2 ConditionalProbabilities 3.3 Bayes'sFormula 3.4 IndependentEvents 3.5 P(·|F)IsaProbability Summary Problems TheoreticalExercises Self-TestProblemsandExercises 4 RandomVariables 4.1 RandomVariables 4.2 DiscreteRandomVariables 4.3 ExpectedValue 4.4 ExpectationofaFunctionofaRandomVariable 4.5 Variance 4.6 TheBernoulhandBinomialRandomVariables 4.6.1 PropertiesofBinomialRandomVariables 4.6.2 ComputingtheBinomialDistributionFunction 4.7 ThePoissonRandomVariable 4.7.1 ComputingthePoissonDistributionFunction 4.8 OtherDiscreteProbabilityDistributions 4.8.1 TheGeometricRandomVariable 4.8.2 TheNegativeBinomialRandomVariable 4.8.3 TheHypergeometricRandomVariable 4.8.4 TheZeta(orZipf)Distribution 4.9 ExpectedValueofSumsofRandomVariables 4.10 PropertiesoftheCumulativeDistributionFunction Summary Problems TheoreticalExercises Self-TestProblemsandExercises 5 ContinuousRandomVariables 51 Introduction 5.2 ExpectationandVarianceofContinuousRandomVariables 5.3 TheUniformRandomVariable 5.4 NormalRandomVariables 5.4.1 TheNormalApproximationtotheBinomialDistribution 5.5 ExponentialRandomVariables 5.5.1 HazardRateFunctions 5.6 OtherContinuousDistributions 5.6.1 TheGammaDlstrlbutlon 5.6.2 TheWeibullDlStrlbutlon 5.6.3 TheCauchyDistribution 5.6.4 TheBetaDlStrlbutlon 5.7 TheDistributionofaFunctionofaRandomVariable Summary Problems TheoreticalExercises Self-TestProblemsandExercises 6 JointlyDistributedRandomVariables 6.1 JointDistributionFunctions 6.2 IndependentRandomVariables 6.3 SumsofIndependentRandomVariables 6.3.1 IdenticallyDistributedUniformRandomVariables 6.3.2 GammaRandomVariables 6.3.3 NormalRandomVariables 6.3.4 PolssonandBinomialRandomVariables 635 GeometricRandomVariables 6.4 ConditionalDistribution：DiscreteCase 6.5 ConditionalDistribution：ContinuousCase 66 OrderStatistics 6.7 JointProbabilityDistributionofFunctionsofRandomVariables 6.8 ExciaanzeaoleRandomVariables Summary Problems TheoreticalExercises SelfTestProblemsandExercises 7 PropertiesofExpectation 7.1 Introduction 7.2 ExpectationofSumsofRandomVariablviatheProbabilisticMethod 7.2.2 TheMaximum-MinimumsIdentity 7.3 MomentsoftheNumberofEventsthatOccur 7.4 Covariance,VarianceofSums,andCorrelations 7.5 ConditionalExpectation 7.5.1 Definitions 7.5.2 ComputingExpectationsbyConditioning 7.5.3 ComputingProbabilitiesbyConditioning 7.5.4 ConditionalVariance 7.6 ConditionalExpectationandPrediction 7.7 MomentGeneratingFunctions 7.7.1 JointMomentGeneratingFunctions 7.8 AddltlonaproprietariesofNormalRandomVariables 7.8.1 TheMultivariateNormalDlstrlbution 7.8.2 TheJointDistributionoftheSampleMeanandSampleVariance 7.9 GeneralDefinitionofExpectation Summary Problems TheoreticalExercises Self-TestProblemsandExercises 8 LimitTheorems 8.1 Introduction 8.2 Chebyshev'sInequalityandtheWeakLawofLargeNumbers 8.3 TheCentralLimitTheorem 8.4 TheStrongLawofLargeNumbers 8.5 OtherInequamles 8.6 BoundingtheErrorProbabilityWhenApproximatingaSumofIndependentBernoulliRandomVariablesbyaPoissonRandomVariable Summary Problems TheoreticalExercises Self-TestProblemsandExercises 9 AdditionalTopicsinProbability 9.1 ThePoissonProcess 9.2 MarkovChains 9.3 Surprise,Uncertainty,andEntropy 9.4 CodingTheoryandEntropy Summary ProblemsandTheoreticalExercises Self-TestProblemsandExercises References 10 Simulation 10.1 Introduction 10.2 GeneralTechniquesforSimulatingContinuousRandomVariables 10.2.1 TheInverseTransformationMethod 10.2.2 TheRejectionMethod 10.3 SimulatingfromDiscreteDistributions 10.4 VarianceReductionTechniques 10.4.1 UseofAntitheticVariables 10.4.2 VarianceReductionbyConditioning 10.4.3 ControlVariates Summary Problems Self-TestProblemsandExercises Reference AnswerstoSelectedProblems SolutionstoSelf-TestProblemsandExercises Index