Copyright©2009CengageLearning6.1ChapterSixProbabilityCopyright©2009CengageLearningAbouttheprobability6.2Inthischapterwelookatthemathematicalstructureoflikelihoodchangeandprobability,processeswhichunderpinalldataanalysis.Afterworkingthroughityoushouldbeableto:Setupmodelstostudydata,Drawinferencesfromdata,Makesensiblejudgementsbasedonyourconclusions,Usethetechniquestogenerateconclusionsandpredictions,drawnfromvariousdatasources.TheLanguageofChanceIneverydayspeechweusedthewords‘possible’and‘probable’toindicatedegreesoflikelihood.Atypicalweatherforecastmaysoundlikethis:‘…thereisaprobabilityofshowersintheeast,but,inthewest,rainisprobablebeforedawn.’Whatdoyouthinktheforecastermeans?Inthelanguageofmathematicalandstatistics,both‘rainintheeast’and‘showersinthewest’areprobabilities,orevents,orsituationsthatcouldoccur.Theforecasterwastryingtoindicatethattherewasachancethateitherwouldhappenbut,thatinheropinion,therewasgreaterlikelihoodof‘raininthewest’.Copyright©2009CengageLearning6.3ApproachestoAssigningProbabilities…Therearethreewaystoassignaprobability,P(Oi),toanoutcome,Oi,namely:Classicalapproach:basedonequallylikelyevents.Relativefrequency:assigningprobabilitiesbasedonexperimentationorhistoricaldata.Subjectiveapproach:Assigningprobabilitiesbasedontheassignor’s(subjective)judgment.Copyright©2009CengageLearning6.4ClassicalApproach…Ifanexperimenthasnpossibleoutcomes,thismethodwouldassignaprobabilityof1/ntoeachoutcome.Itisnecessarytodeterminethenumberofpossibleoutcomes.Experiment:RollingadieOutcomes{1,2,3,4,5,6}Probabilities:Eachsamplepointhasa1/6chanceofoccurring.Copyright©2009CengageLearning6.5ClassicalApproach…Experiment:RollingtwodiceandobservingthetotalOutcomes:{2,3,…,12}Examples:P(2)=1/36P(6)=5/36P(10)=3/36123456123456723456783456789456789105678910116789101112Copyright©2009CengageLearning6.6RelativeFrequencyApproach…Bits&BytesComputerShoptracksthenumberofdesktopcomputersystemsitsellsoveramonth(30days):Forexample,10daysoutof302desktopsw...
