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1、CHAPTERSEVENUncertaintyInthischapterweexploresomeofthebasicelementsofthetheoryofindividualbehaviorinuncertainsituations.Wediscusswhyindividualsdonotlikeriskandthevariousmeth-ods(buyinginsurance,acquiringmoreinformation,andpreservingoptions)theymayadopttoreduceit.Moregenerally,thechapterisintendedtop
2、rovideabriefintroductiontoissuesraisedbythepossibilitythatinformationmaybeimperfectwhenindividualsmakeutility-maximizingdecisions.TheExtensionssectionprovidesadetailedapplicationoftheconceptsinthischaptertotheportfolioproblem,acentralproblemin?nancialeco-nomics.Whetherawell-informedpersoncantakeadva
3、ntageofapoorlyinformedpersoninamarkettransaction(asymmetricinformation)isaquestionputoffuntilChapter18.MathematicalStatisticsManyoftheformaltoolsformodelinguncertaintyineconomicsituationswereoriginallydevelopedinthe?eldofmathematicalstatistics.SomeofthesetoolswerereviewedinChapter2,andinthischapterw
4、ewillmakeagreatdealofuseoftheconceptsintroducedthere.Speci?cally,fourstatisticalideaswillrecurthroughoutthischapter.?Randomvariable:Arandomvariableisavariablethatrecords,innumericalform,1thepossibleoutcomesfromsomerandomevent.?Probabilitydensityfunction(PDF):Afunctionf(x)thatshowstheprobabilitiesass
5、ociatedwiththepossibleoutcomesfromarandomvariable.?Expectedvalueofarandomvariable:Theoutcomeofarandomvariablethatwilloccur‘‘onaverage.’’TheexpectedvalueisdenotedbyE(x).IfxisadiscreterandomPnvariablewithnoutcomes,thenREexT?i?1xifexiT.Ifxisacontinuousrandomt1variable,thenEexT?xfexTdx.%1?Varianceandsta
6、ndarddeviationofarandomvariable:Theseconceptsmeasurethedispersionofarandomvariableaboutitsexpectedvalue.Inthediscretecase,2Pn22VarRexT?rx?i?1?xi%EexTfexiT;inthecontinuouscase,VarexT?rx?t12?x%EexTfexTdx.Thestandarddeviationisthesquarerootofthevariance.%1Asweshallsee,alltheseconceptswillcomeintoplaywh
7、enwebeginlookingatthedeci-sion-makingprocessofapersonfacedwithanumberofuncertainoutcomesthatcanbeconceptuallyrepresentedbyarandomvariable.1~Whenitisnecessarytodistinguishbetweenrandomvariablesandnonra
