lec12 - ContinuousRandomVariables

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Unformatted text preview: ContinuousRandomVariables AllpropertiesofdiscreteRVshavedirectcounterpartsforconinuousRVs. Onebasicdifference: summationsusedinthecaseofdiscreteRVsare replacedbyintegrals. Summingover(uncountable)infinitemanyvaluescorrespondstoanintegral. Fore.g.,wedefineacumulativedistributionfunction(cdf)asfollows: Definition: CDFofa X isacontinuousrandomvariable: Thefunction F X ( t ):= P ( X t ) iscalledthe cumulativedistribution functionof X . Theonlydifferencetothediscretecaseisthatthecdfofacontinuous variableisnotastairstepfunction. 1 Propertiesof F X Thefollowingpropertiesholdforthecumulativedistributionfunction F X forrandomvariable X . F X ( t ) 1 forall t F X ismonotoneincreasing,(i.e.if x 1 x 2 then F X ( x 1 ) F X ( x 2 ) .) lim t F X ( t )=0 and lim t F X ( t )=1 . However,thereisslightdifferencefromthediscretecase: Definition: ProbabilityDensityFunction Foracontinuousvariable X with cumulativedistributionfunction F X the densityfunctionof...
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This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.

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lec12 - ContinuousRandomVariables

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