AppliedaStatisticsaandaProbabilityaforaEngineers,a5thaedition
CHAPTERa2
Sectiona2-1
ProvideaaareasonableadescriptionaofatheasampleaspaceaforaeachaofathearandomaexperimentsainaExercisesa2-1atoa2-
17.aThereacanabeamoreathanaoneaacceptableainterpretationaofaeachaexperiment.aDescribeaanyaassumptionsayouamake.
2-1. Eachaofathreeamachinedapartsaisaclassifiedaasaeitheraaboveaorabelowatheatargetaspecificationaforatheapart.aLeta aaandab
denoteaaapartaaboveaandabelowatheaspecification,arespectively.
S aaaa,aaaba,aabaa,aabba,abaaa,ababa,abbaa,abbba
2-2. Eachaofafouratransmittedabitsaisaclassifiedaasaeitherainaerroraoranotainaerror.
Letaeaandaoadenoteaaabitainaerroraandanotainaerrora(oadenotesaokay),arespectively.
eeeeaeeeoa,a,aeoeeaeoeoa,a,aoeeeaoeeoa,a,aooeea ooeoa,,
S
eeoea,aeooea,aoeoea,aoooea,
eeooa,aeoooa,aoeooa,aooooa
2-3.
Inatheafinalainspectionaofaelectronicapowerasupplies,aeitheraunitsapass,aorathreeatypesaofanonconformitiesamightaoc
cur:afunctional,aminor,aoracosmetic.aThreeaunitsaareainspected.
Letaaadenoteaanaacceptableapowerasupply.
Letaf,am,aandacadenoteaaapowerasupplyathatahasaaafunctional,aminor,aoracosmeticaerror,arespectively.aSa
aa,afa,ama,ac
2-4. Theanumberaofahitsa(views)aisarecordedaataaahigh-volumeaWebasiteainaaaday.
S 0,1,2,... =asetaofanonnegativeaintegers
2-5. Eachaofa24aWebasitesaisaclassifiedaasacontainingaoranotacontainingabanneraads.
Letayaandanadenoteaaawebasiteathatacontainsaandadoesanotacontainabanneraads.
Theasampleaspaceaisatheasetaofaallapossibleasequencesaofayaandanaofalengtha24.aAnaexampleaoutcomeainatheasampleaspaceais
2-1
,AppliedaStatisticsaandaProbabilityaforaEngineers,a5thaedition
S yynnynyyynanynynnnnyyannyya
2-6. Anaammeterathatadisplaysathreeadigitsaisausedatoameasureacurrentainamilliamperes.
Aavectorawithathreeacomponentsacanadescribeatheathreeadigitsaofatheaammeter.aEachadigitacanabea0,1,2,...,9.a
TheasampleaspaceaSaisa1000apossibleathreeadigitaintegers,aS 000a,001a,...,a999a
2-7. Aascaleathatadisplaysatwoadecimalaplacesaisausedatoameasureamaterialafeedsainaaachemicalaplantainatons.
Saisatheasampleaspaceaofa100apossibleatwoadigitaintegers.
2-
8.aTheafollowingatwoaquestionsaappearaonaanaemployeeasurveyaquestionnaire.aEachaansweraisachosenafromatheafiveap
ointascalea1a(never),a2,a3,a4,a5a(always).
Isatheacorporationawillingatoalistenatoaandafairlyaevaluateanewaideas?aHo
waoftenaareamyacoworkersaimportantainamyaoverallajobaperformance?
Letaanaorderedapairaofanumbers,asuchaasa43adenoteathearesponseaonatheafirstaandasecondaquestion.aThen,aSaconsistsa
ofathea25aorderedapairsa 1a1,12,a.a.a.a,55
2-9. Theaconcentrationaofaozoneatoatheanearestapartaperabillion.
S 0a,1,2,...,1Ea09 inappb.
2-10. Theatimeauntilaaaserviceatransactionaisarequestedaofaaacomputeratoatheanearestamillisecond.
S 0a,1,2a,..., inamilliseconds
2-11. TheapHareadingaofaaawaterasampleatoatheanearestatenthaofaaaunit.
S 1a.0a,1a.1,1a.2a,a…a14a.0
2-12.
Theavoidsainaaaferriteaslabaareaclassifiedaasasmall,amedium,aoralarge.aTheanumberaofavoidsainaeachacategorya
isameasuredabyaanaopticalainspectionaofaaasample.
Letas,am,aandaladenoteasmall,amedium,aandalarge,arespectively.aThenaSa=a{s,am,al,ass,asm,asl,a….}a
2-13 Theatimeaofaaachemicalareactionaisarecordedatoatheanearestamillisecond.
S 0a,1,2a,..., inamilliseconds.
2-
14.aAnaorderaforaanaautomobileacanaspecifyaeitheraanaautomaticaoraaastandardatransmission,aeitherawithaorawithoutaairac
onditioning,aandawithaanyaoneaofatheafouracolorsared,ablue,ablack,aorawhite.aDescribeatheasetaofapossibleaordersaforathisae
xperiment.
,2-2
, AppliedaStatisticsaandaProbabilityaforaEngineers,a5thaedition
automatic standard
a transmissio
a transmissi
n
on
with with without
a ai without a ai a ai
r a air r r
redablueablacka a white redablueablack whitea a redablueablack white redablueablack white
2-15.aAasampledainjection-
moldedapartacouldahaveabeenaproducedainaeitheraoneaofatwoapressesaandainaanyaoneaofatheaeightacavitiesainaeachapress.
PaRESaS 1
2
CaAVIaTY
1a a 2a a 3 4 5 6a a 7a a 8 1 2 3 4 5 6 7 8
2-16.
Anaorderaforaaacomputerasystemacanaspecifyamemoryaofa4,a8,aora12agigabytesaandadiskastorageaofa200,a300,aora40
0agigabytes.aDescribeatheasetaofapossibleaorders.
memory
4 8 12
diskastorage
200 300 400 200 300 400 200 300 400
2-17. Callsaarearepeatedlyaplacedatoaaabusyaphonealineauntilaaaconnectionaisaachieved.
Letacaandabadenoteaconnectaandabusy,arespectively.aThenaSa=a{c,abc,abbc,abbbc,abbbbc,a…}
2-18.
Threeaattemptsaareamadeatoareadadataainaaamagneticastorageadeviceabeforeaanaerrorarecoveryaprocedureathatarepositio
nsatheamagneticaheadaisaused.aTheaerrorarecoveryaprocedureaattemptsathreearepositioningsabeforeaana“abort’’amessageai
sasentatoatheaoperator.aLet
sadenoteatheasuccessaofaaareadaoperationa f
denoteatheafailureaofaaareadaoperation
2-3
CHAPTERa2
Sectiona2-1
ProvideaaareasonableadescriptionaofatheasampleaspaceaforaeachaofathearandomaexperimentsainaExercisesa2-1atoa2-
17.aThereacanabeamoreathanaoneaacceptableainterpretationaofaeachaexperiment.aDescribeaanyaassumptionsayouamake.
2-1. Eachaofathreeamachinedapartsaisaclassifiedaasaeitheraaboveaorabelowatheatargetaspecificationaforatheapart.aLeta aaandab
denoteaaapartaaboveaandabelowatheaspecification,arespectively.
S aaaa,aaaba,aabaa,aabba,abaaa,ababa,abbaa,abbba
2-2. Eachaofafouratransmittedabitsaisaclassifiedaasaeitherainaerroraoranotainaerror.
Letaeaandaoadenoteaaabitainaerroraandanotainaerrora(oadenotesaokay),arespectively.
eeeeaeeeoa,a,aeoeeaeoeoa,a,aoeeeaoeeoa,a,aooeea ooeoa,,
S
eeoea,aeooea,aoeoea,aoooea,
eeooa,aeoooa,aoeooa,aooooa
2-3.
Inatheafinalainspectionaofaelectronicapowerasupplies,aeitheraunitsapass,aorathreeatypesaofanonconformitiesamightaoc
cur:afunctional,aminor,aoracosmetic.aThreeaunitsaareainspected.
Letaaadenoteaanaacceptableapowerasupply.
Letaf,am,aandacadenoteaaapowerasupplyathatahasaaafunctional,aminor,aoracosmeticaerror,arespectively.aSa
aa,afa,ama,ac
2-4. Theanumberaofahitsa(views)aisarecordedaataaahigh-volumeaWebasiteainaaaday.
S 0,1,2,... =asetaofanonnegativeaintegers
2-5. Eachaofa24aWebasitesaisaclassifiedaasacontainingaoranotacontainingabanneraads.
Letayaandanadenoteaaawebasiteathatacontainsaandadoesanotacontainabanneraads.
Theasampleaspaceaisatheasetaofaallapossibleasequencesaofayaandanaofalengtha24.aAnaexampleaoutcomeainatheasampleaspaceais
2-1
,AppliedaStatisticsaandaProbabilityaforaEngineers,a5thaedition
S yynnynyyynanynynnnnyyannyya
2-6. Anaammeterathatadisplaysathreeadigitsaisausedatoameasureacurrentainamilliamperes.
Aavectorawithathreeacomponentsacanadescribeatheathreeadigitsaofatheaammeter.aEachadigitacanabea0,1,2,...,9.a
TheasampleaspaceaSaisa1000apossibleathreeadigitaintegers,aS 000a,001a,...,a999a
2-7. Aascaleathatadisplaysatwoadecimalaplacesaisausedatoameasureamaterialafeedsainaaachemicalaplantainatons.
Saisatheasampleaspaceaofa100apossibleatwoadigitaintegers.
2-
8.aTheafollowingatwoaquestionsaappearaonaanaemployeeasurveyaquestionnaire.aEachaansweraisachosenafromatheafiveap
ointascalea1a(never),a2,a3,a4,a5a(always).
Isatheacorporationawillingatoalistenatoaandafairlyaevaluateanewaideas?aHo
waoftenaareamyacoworkersaimportantainamyaoverallajobaperformance?
Letaanaorderedapairaofanumbers,asuchaasa43adenoteathearesponseaonatheafirstaandasecondaquestion.aThen,aSaconsistsa
ofathea25aorderedapairsa 1a1,12,a.a.a.a,55
2-9. Theaconcentrationaofaozoneatoatheanearestapartaperabillion.
S 0a,1,2,...,1Ea09 inappb.
2-10. Theatimeauntilaaaserviceatransactionaisarequestedaofaaacomputeratoatheanearestamillisecond.
S 0a,1,2a,..., inamilliseconds
2-11. TheapHareadingaofaaawaterasampleatoatheanearestatenthaofaaaunit.
S 1a.0a,1a.1,1a.2a,a…a14a.0
2-12.
Theavoidsainaaaferriteaslabaareaclassifiedaasasmall,amedium,aoralarge.aTheanumberaofavoidsainaeachacategorya
isameasuredabyaanaopticalainspectionaofaaasample.
Letas,am,aandaladenoteasmall,amedium,aandalarge,arespectively.aThenaSa=a{s,am,al,ass,asm,asl,a….}a
2-13 Theatimeaofaaachemicalareactionaisarecordedatoatheanearestamillisecond.
S 0a,1,2a,..., inamilliseconds.
2-
14.aAnaorderaforaanaautomobileacanaspecifyaeitheraanaautomaticaoraaastandardatransmission,aeitherawithaorawithoutaairac
onditioning,aandawithaanyaoneaofatheafouracolorsared,ablue,ablack,aorawhite.aDescribeatheasetaofapossibleaordersaforathisae
xperiment.
,2-2
, AppliedaStatisticsaandaProbabilityaforaEngineers,a5thaedition
automatic standard
a transmissio
a transmissi
n
on
with with without
a ai without a ai a ai
r a air r r
redablueablacka a white redablueablack whitea a redablueablack white redablueablack white
2-15.aAasampledainjection-
moldedapartacouldahaveabeenaproducedainaeitheraoneaofatwoapressesaandainaanyaoneaofatheaeightacavitiesainaeachapress.
PaRESaS 1
2
CaAVIaTY
1a a 2a a 3 4 5 6a a 7a a 8 1 2 3 4 5 6 7 8
2-16.
Anaorderaforaaacomputerasystemacanaspecifyamemoryaofa4,a8,aora12agigabytesaandadiskastorageaofa200,a300,aora40
0agigabytes.aDescribeatheasetaofapossibleaorders.
memory
4 8 12
diskastorage
200 300 400 200 300 400 200 300 400
2-17. Callsaarearepeatedlyaplacedatoaaabusyaphonealineauntilaaaconnectionaisaachieved.
Letacaandabadenoteaconnectaandabusy,arespectively.aThenaSa=a{c,abc,abbc,abbbc,abbbbc,a…}
2-18.
Threeaattemptsaareamadeatoareadadataainaaamagneticastorageadeviceabeforeaanaerrorarecoveryaprocedureathatarepositio
nsatheamagneticaheadaisaused.aTheaerrorarecoveryaprocedureaattemptsathreearepositioningsabeforeaana“abort’’amessageai
sasentatoatheaoperator.aLet
sadenoteatheasuccessaofaaareadaoperationa f
denoteatheafailureaofaaareadaoperation
2-3
