应用概率论

Preface
IBasicProbability
1TrialsandEvents
1.1Trials,Outcomes,andEvents
1.2CombinationsofEventsandSpecialEvents
1.3IndicatorFunctionsandCombinationsofEvents
1.4Classes,Partitions,andBooleanCombinations
2ProbabilitySystems
2.1ProbabilityMeasures
2.2SomeElementaryProperties
2.3InterpretationandDeterminationofProbabilities
2.4MintermMapsandBooleanCombinations
2aTheSigmaAlgebraofEvents
3ConditionalProbability
3.1ConditioningandtheReassignmentofLikelihoods
3.2PropertiesofConditionalProbability
3.3RepeatedConditioning
4IndependenceofEvents
4.1IndependenceasaLackofConditioning
4.2IndependentClasses
5ConditionalIndependenceofEvents
5.1OperationalIndependenceandaCommonCondition
5.2EquivalentConditionsandDefinition
5.3SomeProblemsinProbableInference
5.4ClassificationProblems
6CompositeTrials
6.1EventsandComponentEvents
6.2MultipleSuccess-FailureTrials
6.3BernoulliTrials
IIRandomVariablesandDistributions
RandomVariablesandProbabilities
7.1RandomVariablesasFunctions--MappingConcepts
7.2MassTransferandProbabilityDistributions
7.3SimpleRandomVariables
7aBorelSets,RandomVariables,andBorelFunctions
8DistributionandDensityFunctions
8.1TheDistributionFunction
8.2SomeDiscreteDistributions
8.3AbsolutelyContinuousRandomVariablesandDensityFunc-
tions
8.4SomeAbsolutelyContinuousDistributions
8.5TheNormalDistribution
8.6LifeDistributionsinReliabilityTheory
9RandomVectorsandJointDistributions
9.1TheJointDistributionDeterminedbyaRandomVector
9.2TheJointDistributionFunctionandMarginalDistributions
9.3JointDensityFunctions
10IndependenceofRandomVectors
10.1IndependenceofRandomVectors
10.2SimpleRandomVariables
10.3JointDensityFunctionsandIndependence
11FunctionsofRandomVariables
11.1AFundamentalApproachandsomeExamples
11.2FunctionsofMoreThanOneRandomVariable
11.3FunctionsofIndependentRandomVariables
11.4TheQuantileFunction
11.5CoordinateTransformations
11aSomePropertiesoftheQuantileFunction
IIIMathematicalExpectation
12MathematicalExpectation
12.1TheConcept
12.2TheMeanValueofaRandomVariable
13ExpectationandIntegrals
13.1ASketchoftheDevelopment
13.2IntegralsofSimpleFunctions
13.3IntegralsofNonnegativeFunctions
13.4IntegrableFunctions
13.5MathematicalExpectationandtheLebesgueIntegral
13.6TheLebesgue-StieltjesIntegralandTransformationofIn-
tegrals
13.7SomePurtherPropertiesofIntegrals
13.8TheRadon-NikodymTheoremandFubini'sTheorem
13.9IntegralsofComplexRandomVariablesandtheVector
SpaceL2
13aSupplementaryTheoreticalDetails
13a.1IntegralsofSimpleFunctions
13a.2IntegralsofNonnegativeFunctions
13a.3IntegrableFunctions
14PropertiesofExpectation
14.1SomeBasicFormsofMathematicalExpectation
14.2ATableofProperties
14.3IndependenceandExpectation
14.4SomeAlternateFormsofExpectation
14.5ASpecialCaseoftheRadon-NikodymTheorem
15VarianceandStandardDeviation
15.1VarianceasaMeasureofSpread
15.2SomeProperties
15.3VariancesforSomeCommonDistributions
15.4StandardizedVariablesandtheChebyshevInequality
16Covariance,Correlation,andLinearRegression
16.1CovarianceandCorrelation
16.2SomeExamples
16.3LinearRegression
17ConvergenceinProbabilityTheory
17.1SequencesofEvents
17.2AlmostSureConvergence
17.3ConvergenceinProbability
17.4ConvergenceintheMean
17.5ConvergenceinDistribution
18TransformMethods
18.1ExpectationsandIntegralTransforms
18.2TransformsforSomeCommonDistributions
18.3GeneratingFunctionsforNonnegative,Integer-ValuedRan-
domVariables
18.4MomentGeneratingFunctionandtheLaplaceTransform
18.5CharacteristicFunctions
18.6TheCentralLimitTheorem
18.7RandomSamplesandStatistics
IVConditionalExpectation
19ConditionalExpectation,GivenaRandomVector
19.1ConditioningbyanEvent
19.2ConditioningbyaRandomVector--SpecialCases
19.3ConditioningbyaRandomVector--GeneralCase
19.4PropertiesofConditionalExpectation
19.5RegressionandMean-SquareEstimation
19.6InterpretationinTermsofHilbertSpaceL2
19.7SumsofRandomVariablesandConvolution
19aSomeTheoreticalDetails
20RandomSelectionandCountingProcesses
20.1IntroductoryExamplesandaFormalRepresentation
20.2IndependentSelectionfromanIidSequence
20.3APoissonDecompositionResult--MultinomialTrials
20.4ExtremeValues
20.5BernoulliTrialswithRandomExecutionTimes
20.6ArrivalTimesandCountingProcesses
20.7ArrivalsandDemandinanIndependentRandomTimePe-
riod
20.8DecisionSchemesandMarkovTimes
21PoissonProcesses
21.1TheHomogeneousPoissonProcess
21.2ArrivalsofmkindsandcompoundPoissonprocesses
21.3SuperpositionofPoissonProcesses
21.4ConditionalOrderStatistics
21.5NonhomogeneousPoissonProcesses
21.6BibliographicNote
21a
21a.1IndependentIncrements
21a.2AxiomSystemsfortheHomogeneousPoissonProcess
22ConditionalIndependence,GivenaRandomVector
22.1TheConceptandSomeBasicProperties
22.2TheBayesianApproachtoStatistics
22.3ElementaryDecisionModels
22aProofsofProperties
23MarkovSequences
23.1TheMarkovPropertyforSequences
23.2SomeFurtherPatternsandExamples
23.3TheChapman-KolmogorovEquation
23.4TheTransitionDiagramandtheTransitionMatrix
23.5VisitstoaGivenStateinaHomogeneousChain
23.6ClassificationofStatesinHomogeneousChains
23.7RecurrentStatesandLimitProbabilities
23.8PartitioningFiniteHomogeneousChains
23.9EvolutionofFinite,ErgodicChains
23.10TheStrongMarkovPropertyforSequences
23aSomeTheoreticalDetails
ASomeMathematicalAids
BSomeBasicCountingProblems
Index