应用概率论

Preface
I  BasicProbability
  1 TrialsandEvents
    1.1 Trials,Outcomes,andEvents
    1.2 CombinationsofEventsandSpecialEvents
    1.3 IndicatorFunctionsandCombinationsofEvents
    1.4 Classes,Partitions,andBooleanCombinations
  2 ProbabilitySystems
    2.1 ProbabilityMeasures
    2.2 SomeElementaryProperties
    2.3 InterpretationandDeterminationofProbabilities
    2.4 MintermMapsandBooleanCombinations
  2a TheSigmaAlgebraofEvents
  3 ConditionalProbability
    3.1 ConditioningandtheReassignmentofLikelihoods
    3.2 PropertiesofConditionalProbability
    3.3 RepeatedConditioning
  4 IndependenceofEvents
    4.1 IndependenceasaLackofConditioning
    4.2 IndependentClasses
  5 ConditionalIndependenceofEvents
    5.1 OperationalIndependenceandaCommonCondition
    5.2 EquivalentConditionsandDefinition
    5.3 SomeProblemsinProbableInference
    5.4 ClassificationProblems
  6 CompositeTrials
    6.1 EventsandComponentEvents
    6.2 MultipleSuccess-FailureTrials
    6.3 BernoulliTrials
II  RandomVariablesandDistributions
  7 RandomVariablesandProbabilities
    7.1 RandomVariablesasFunctions--MappingConcepts
    7.2 MassTransferandProbabilityDistributions
    7.3 SimpleRandomVariables
  7a BorelSets,RandomVariables,andBorelFunctions
  8 DistributionandDensityFunctions
    8.1 TheDistributionFunction
    8.2 SomeDiscreteDistributions
    8.3 AbsolutelyContinuousRandomVariablesandDensityFunc-tions
    8.4 SomeAbsolutelyContinuousDistributions
    8.5 TheNormalDistribution
    8.6 LifeDistributionsinReliabilityTheory
  9 RandomVectorsandJointDistributions
    9.1 TheJointDistributionDeterminedbyaRandomVector
    9.2 TheJointDistributionFunctionandMarginalDistributions
    9.3 JointDensityFunctions
  10 IndependenceofRandomVectors
    10.1 IndependenceofRandomVectors
    10.2 SimpleRandomVariables
    10.3 JointDensityFunctionsandIndependence
  11 FunctionsofRandomVariables
    11.1 AFundamentalApproachandsomeExamples
    11.2 FunctionsofMoreThanOneRandomVariable
    11.3 FunctionsofIndependentRandomVariables
    11.4 TheQuantileFunction
    11.5 CoordinateTransformations
  11a SomePropertiesoftheQuantileFunction
III  MathematicalExpectation
  12 MathematicalExpectation
    ……
  13 ExpectationandIntegrals
  14 PropertiesofExpectation
  15 VarianceandStandardDeviation
  16 Covariance,Correlation,andLinearRegression
  17 ConvergenceinProbabilityTheory
  18 TransformMethods
  19 ConditionalExpectation,GivenaRandomVector
  20 RandomSelectionandCountingProcesses
  21 PoissonProcesses
  21a
  22 ConditionalIndependence,GivenaRandomVector
  23 MarkovSequences
  23a SomeTheoreticalDetails
A SomeMathematicalAids
B SomeBasicCountingProblems
Index