ST259 Chapter Notes - Chapter 3: Sample Space, Pcx
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Defafor a given samplespace 8 ofsomeexperiment a randomvariablecru is anyrule that associates a numberwith each outcome in si in mathematical language arandom variable is afunctionwhosedomainisthe samplespaceandwhoserange is theset ofreal numbers. Defeanyrandomvariablewhoseonly possible values are oand i is called a bernoullirandom. Defi variable discreterandom variable is an rv whosepossiblevalueseitherconstitute a finite set or else can be listed in an infinite sequence in whichthere is afirst element a second element and so on. Its setofpossiblevaluesconsistseitherofall numbersin a sink interval onthe numberline or all numbers in a disjointunionofsuchintervals eg 0,10740,30. Theprobability distributionof x sayshowthetotal probabilityof1 is distributed allocatedto thevarious possiblex values among. Thepmfofanybernoulli rv canbeexpressedintheform p d d andp o l d where 0l x c l. Becausethepmf depends ontheparticularvalueof a weoftenwrite p x dratherthanjust p x pariah. Defatopposepcx depends on a quantitythatcanbeassignedanyoneof a numberofpossiblevalues witheach differentvaluedetermining a differentprobability distribution sucha quantity iscalled a parameterofthe distributionthecollection ofall probabilitydistributionsfordifferentvaluesoftheparameter is called a familyofprobabilitydistributions.
