Probability review for Actuaries P exam

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1、AProbabilityCoursefortheActuariesAPreparationforExamP/1MarcelB.FinanArkansasTechUniversitycAllRightsReservedPreliminaryDraft2InmemoryofmymotherAugust1,2008ContentsPreface7RiskManagementConcepts......................8BasicOperationsonSets111BasicDefinitions......................

2、.....122SetOperations............................19CountingandCombinatorics333TheFundamentalPrincipleofCounting..............334PermutationsandCombinations...................395PermutationsandCombinationswithIndistinguishableObjects.49Probability:DefinitionsandProperties596Basi

3、cDefinitionsandAxiomsofProbability............597PropertiesofProbability.......................678ProbabilityandCountingTechniques................75ConditionalProbabilityandIndependence819ConditionalProbabilities.......................8110PosteriorProbabilities:Bayes’Formula...

4、...........8911IndependentEvents.........................10012OddsandConditionalProbability.................109DiscreteRandomVariables11313RandomVariables..........................11314ProbabilityMassFunctionandCumulativeDistributionFunction11815ExpectedValueofaDiscreteRandomV

5、ariable..........12616ExpectedValueofaFunctionofaDiscreteRandomVariable..13334CONTENTS17VarianceandStandardDeviation.................14018BinomialandMultinomialRandomVariables...........14619PoissonRandomVariable......................16020OtherDiscreteRandomVariables..........

6、.......17020.1GeometricRandomVariable................17020.2NegativeBinomialRandomVariable............17720.3HypergeometricRandomVariable.............18421PropertiesoftheCumulativeDistributionFunction.......190ContinuousRandomVariables20522DistributionFunctions................

7、.......20523Expectation,VarianceandStandardDeviation..........21724TheUniformDistributionFunction................23525NormalRandomVariables.....................24026ExponentialRandomVariables...................25527GammaandBetaDistributions..................26528TheDistributio

8、nofaFunctionofaRandomVariable......277JointDistributions28529