連續型特殊分配1.為指數分數，，試問_________。2.Supposethatlifeofacertaintypeofelectroniccomponenthasanexponentialdistributionwithameanlifeof600hours.Considerthesituationthatthecomponenthasbeeninoperationfor400hours.Pleasefindouttheconditionalprobabilitythatitwilllastforanother600hours.3.Supposethattheamountoftimethatalightbulbworksbeforeburningitselfoutisexponentiallydistributedwithmeaneighthours.SupposethatPeggyentersaroominwhichalighbulbisburning.Shedesirestoworkforfivehours.Theprobabilitythatshewillbeabletocompleteherworkwithoutthebulbburningoutis__________.4.ThecollegeofmanagementatNationalChungChengUniversityrequiresaminimumtestscoreof26.Thetestscoreamonghighschoolseniorsinagivenschooldistrictisnormallydistributedwithmean22andstandarddeviation2.Thepercentageofhighschoolseniorswhoarepotentialrecruitsis__________.5.Exhibit2Theexpectancyofaparticularbrandoftireisnormallydistributedwithameanof40,000andstandarddeviationof5,000miles.(1)RefertoExhibit2.Whatistheprobabilitythatarandomlyselectedtirewillhavealifeofatleast30,000miles？(A)0.4772(B)0.9772(C)0.0228(D)0.5000(2)RefertoExhibit2.Whatispercentageoftireswillhavealifeof34,000to46,000miles？(A)38.49%(B)76.98%(C)50%(D)88.49%(3)RefertoExhibit2.Whatistheprobabilitythatarandomlyselectedtirewillhavealifeofexactly47,500miles？(A)0.0000(B)0.9332(C)0.0668(D)0.49936.Todescribedistributionofthecharacteristicsofthedatacollected,wemayusetheso-calledempiricalrule(i.e.approachinganormaldistribution)andBienayme-ChebyshevRule.Iftheaverageandthestandarddeviationofthescoreofstatisticalcourseare76and7.determineifthefollowingtwodata98and58areoutliers？(None：Itisdefinedthatadatumisregardedasanoutliersiftheprobabilityofoccurrenceislessthan1%)7.Suppose40%ofallcollegestudentshaveacomputerathomeandasampleof64taken.Whatistheprobabilitythatmorethan30ofthoseinthesamplehaveacomputerathome？(A)0.3686(B)0.1314(C)0.8686(D)0.6314(E)Noneoftheabove.8.設為連續的隨機變數，其機率密度函數為：試求：(1)，其中、。(2)條件機率。9.Supposethatarei.i.d.randomvariableswithdistribution.Thentheprobabilitydensityofwhenandwhenis(A)thesame(B)different(C)notcomparable(D)Noneoftheaboveanswersarecorrect.10.Ifhasanexponentialdistribution,showthat.11.Agrapefruitjuiceproducerbuysallhisgrapefruitsfromalargegrapefruitgrove.Theamountofjuicesqueezedfromeachofthesegrapefruitsisapproximatelynormallydistributedwithameanof10.0ouncesandastandarddeviationof1.0ounce.(1)Whatistheprobabilitythatarandomlyselectedgrapefruitwillcontainbetween9.5and11.00ounces？(2)80%ofthegrapefruitswillcontainatleasthowmanyouncesofjuice？(3)Ifrandomsamplesof20grapefruitsareselected,whatistheprobabilitythatthesamplemeanwouldbebetween9.5and11.0ounces？(4)Supposethepopulationmeanandstandarddeviationoftheamountofjuicesqueezedfromthegrapefruitsareunknown,andasampleof6grapefruitsisselectedfromthepopulation.Theamountsofjuicesqueezedfromthose6grapefruitsare9.1,10.1,9.3,9.1,9.8,and9.6ounces.Constructthe95%confidenceintervalforthepopulationmean.12.Letbeuniformlydistributedbetweenandandsymmetricaboutzerowithvariance1.Whatisthevalueof？(A)2(B)4(C)6(D)8(E)1013.某公司各項產品每月銷售量都呈現常態分配。產品的常態分配是，產品的常態分配是，產品的常態分配是，各項產品的銷售量彼此不會互相影響，亦即三者相互獨立，請問：(1)公司每月平均銷售量為何？(2)公司每月銷售量的標準差為何？(3)每月總銷售量低於270的機率為何？14.Supposeisarandomvariablebestdescribedbyuniformprobabilitydistributionwithand.(1)Find(2)Findthemeanandstandarddeviationof.(3)Graph.andlocateandtheintervalonthegraph.15.Electroniccomponentsofacertaintypehavealengthoflifewithprobabilitydensitygivenby：(1)Supposethattwosuchcomponentsoperateindependentlyandinseriesinacertainsystem(thatis,thesystemfailswheneithercomponentfails).Findthedensityfunctionfor,thelengthoflifeofthesystem.(2)Supposethattwosuchcomponentsoperateinparallel(thatis,thesystemdoesnotfailuntilbothcomponentsfail).Finddensityfunctionfor,thelengthofliftofthesystem.
