Springer Texts in Statistics
m m m
Advisors:
Georgem Casella m m Stephen m Fienbergm m Ingram m Olkin
,F.M. Dekking C. Kraaikamp
m m
H.P. Lopuhaä L.E. Meester
m m
A Modern Introduction to Prob
m m m m
ability and Statistics
m m
Understanding Why and How
m m m
With m 120 m Figures
,FrederikmMichelmDekkingm
Cornelis mKraaikampmHendr
ikmPaulmLopuhaa¨mLudolfm
ErwinmMeester
DelftmInstitutemofmAppliedmMathematics m
DelftmUniversitymofmTechnologymMekel
wegm4
2628mCD mDelft
mThemNetherlan
ds
Whilstmwemhavemmademconsiderablemefforts mto mcontactmallmholders mof mcopyrightmmaterialmcontained m
in mthis m book,m wemmay m havem failed m to m locatemsomemofm them. m Should mholders m wish m to m contactm t
hem Publisher, m wem willmbemhappy mto mcomemto msomemarrangementmwith mthem.
British mLibrary mCataloguingmin mPublication mData
Ammodern mintroduction mto mprobability mand mstatistics. m—
m (Springer mtexts min mstatistics)
1.m Probabilities m m 2.m Mathematicalm statistics
I.m Dekking, m F.m
M.
519.2
ISBNm1852338962
Library mof mCongress mCataloging-in-Publication mData
Ammodern mintroduction mto mprobability mand mstatistics m:munderstandingmwhy mand mhowm/mF.M.mDekkin
gm...m[etm al.].
p.mcm.m—
m(Springer mtextsminmstatistics) m Includesmbiblio
graphicalmreferences mand mindex. m ISBNm1-
85233-896-2
1.mProbabilities—Textbooks. m 2.mMathematicalmstatistics—
Textbooks. m I.mDekking, mF.M.m II.m Series.
QA273.M645 m m 2005
519.2—dc22 2004057700
Apartmfrom many mfair mdealingmfor mthempurposes mof mresearch mor mprivatemstudy,mor mcriticism mor mreview
,mas m permitted munder mthemCopyright, mDesigns mand mPatents mActm1988,mthis mpublication mmay monly mb
emreproduced,m stored mor mtransmitted, min many mform mor mby many mmeans,mwith mthemprior mpermission min
mwritingmof mthempublish-
m ers, mor min mthemcasemof mreprographic mreproduction min maccordance mwith mthemterms mof mlicences missue
d mby mthem CopyrightmLicensingmAgency. mEnquiries mconcerningmreproduction moutsidemthosemterms msh
ould mbemsentmto m thempublishers.
ISBN-10:m1-85233-896-2
ISBN-13:m 978-1-85233-896-1
Springer mScience+BusinessmMediam springero
nline.com
©mSpringer-VerlagmLondon mLimited m2005
Themusem of m registered m names,m trademarks, m etc.m in m this mpublication m does mnotm imply,m even m in m the
m absencem of mamspecificmstatement, mthatmsuch mnames maremexemptmfrom mthemrelevantmlaws mand mregul
ations mand mthereforem freemfor mgeneralmuse.
Thempublisher mmakes mno mrepresentation, mexpress mor mimplied, mwith mregard mto mthemaccuracy mof mthemi
nforma-
m tion mcontained min mthis mbook mand mcannotmacceptmany mlegalmresponsibility mor mliability mfor many merror
s mor m omissions mthatmmay mbemmade.
Printed m in m them United m States m of m America
12/3830/543210 m m Printed m on m acid-freem paper m m SPINm 10943403
, Preface
Probability mandmstatistics maremfascinatingmsubjects monmtheminterfacembetween
mmathematics mandm appliedmsciences m thatmhelpmus munders tandmandmsolvempra
ctical mproblems. mWembelievem thatmyou, mby mlearningmhowmstochastic mmethods
mcomemaboutmandmwhy mthey mwork, mwill mbemablemtomunders tandmthemmeaning
mofmstatistical mstatements mas m well mas mjudgemthemquality mofmtheirmcontent, mwh
enmfacingmsuchmprobl ems monmyourmown. mOurmphilosophy mis monemofmhowm and
mwhy:minsteadmofmjus tmpresentingmstochas tic mmethods mas mcookbook mrecipes, m
wemprefermtomexplainmthemprinciples mbehi ndm them.
Inmthis mbookmyoumwill mfindmthembasics mofmprobability mtheory mandmstatistics. mI
nmaddi tion, m therem arem s everal mtopics m thatm gom somewhatmbeyondm them basi
cs m butmthatmoughtmtombempresentminmanmintroductory mcourse:msimulation, mthe
mPoissonmprocess, mthemlawmofmlargem numbers, mandmthemcentral mlimitmtheorem.
mComputers mhavembroughtmmany mchanges m inmstatistics. mInmparticul ar, m thembo
otstrapmhas mearnedmits mplace. mItmprovides mthempossibility mtomderivemconfiden
cemintervals mandmperformmtes ts mofmhypothes es mwheremtradi tional m(normal map
proximationmormlargemsample)mmethods mareminappropri ate. mItmis mammodernmu
seful mtool monemshouldmlearnmabout, mwembelieve.
Examples mandmdatas ets minmthis mbookmaremmostly mfrommreal-
lifemsituations, matm leastmthatmis mwhatmwemlookedmforminmillustrations mofmthem
material.mAnybody mwhomhas minspectedmdatasets mwithmthempurposemofmusingmt
hemmas melementary mexamples mknows mthatmthis mis mhard:monmthemonemhand, my
oumdomnotmwantmtomboldly mstatemassumptions mthatmaremclearly mnotmsatisfied;m
onmthemothermhand, mlongmexplanations mconcerningmsidem issues mdistractmfromm
them mainm points. m Wem hopemthatmwemfoundm amgoodmmiddlemway.
Amfirstmcourseminmcalculus mis mneededmas mamprerequisitemformthis mbook. mInmad
ditionmtomhigh-
school malgebra, msomeminfinitemseri es maremusedm(exponential, mgeometric). mInte
grationmandmdifferenti ationm aremthemmostmimportantmskills,mmainly mconcern-
mingmonemvariablem(themexceptions, mtwomdimensional mintegrals, maremencounter
edminmChapters m 9–
11). m Althoughm them mathematics m is m keptm tom am minimum,m wem strived
m m m
Advisors:
Georgem Casella m m Stephen m Fienbergm m Ingram m Olkin
,F.M. Dekking C. Kraaikamp
m m
H.P. Lopuhaä L.E. Meester
m m
A Modern Introduction to Prob
m m m m
ability and Statistics
m m
Understanding Why and How
m m m
With m 120 m Figures
,FrederikmMichelmDekkingm
Cornelis mKraaikampmHendr
ikmPaulmLopuhaa¨mLudolfm
ErwinmMeester
DelftmInstitutemofmAppliedmMathematics m
DelftmUniversitymofmTechnologymMekel
wegm4
2628mCD mDelft
mThemNetherlan
ds
Whilstmwemhavemmademconsiderablemefforts mto mcontactmallmholders mof mcopyrightmmaterialmcontained m
in mthis m book,m wemmay m havem failed m to m locatemsomemofm them. m Should mholders m wish m to m contactm t
hem Publisher, m wem willmbemhappy mto mcomemto msomemarrangementmwith mthem.
British mLibrary mCataloguingmin mPublication mData
Ammodern mintroduction mto mprobability mand mstatistics. m—
m (Springer mtexts min mstatistics)
1.m Probabilities m m 2.m Mathematicalm statistics
I.m Dekking, m F.m
M.
519.2
ISBNm1852338962
Library mof mCongress mCataloging-in-Publication mData
Ammodern mintroduction mto mprobability mand mstatistics m:munderstandingmwhy mand mhowm/mF.M.mDekkin
gm...m[etm al.].
p.mcm.m—
m(Springer mtextsminmstatistics) m Includesmbiblio
graphicalmreferences mand mindex. m ISBNm1-
85233-896-2
1.mProbabilities—Textbooks. m 2.mMathematicalmstatistics—
Textbooks. m I.mDekking, mF.M.m II.m Series.
QA273.M645 m m 2005
519.2—dc22 2004057700
Apartmfrom many mfair mdealingmfor mthempurposes mof mresearch mor mprivatemstudy,mor mcriticism mor mreview
,mas m permitted munder mthemCopyright, mDesigns mand mPatents mActm1988,mthis mpublication mmay monly mb
emreproduced,m stored mor mtransmitted, min many mform mor mby many mmeans,mwith mthemprior mpermission min
mwritingmof mthempublish-
m ers, mor min mthemcasemof mreprographic mreproduction min maccordance mwith mthemterms mof mlicences missue
d mby mthem CopyrightmLicensingmAgency. mEnquiries mconcerningmreproduction moutsidemthosemterms msh
ould mbemsentmto m thempublishers.
ISBN-10:m1-85233-896-2
ISBN-13:m 978-1-85233-896-1
Springer mScience+BusinessmMediam springero
nline.com
©mSpringer-VerlagmLondon mLimited m2005
Themusem of m registered m names,m trademarks, m etc.m in m this mpublication m does mnotm imply,m even m in m the
m absencem of mamspecificmstatement, mthatmsuch mnames maremexemptmfrom mthemrelevantmlaws mand mregul
ations mand mthereforem freemfor mgeneralmuse.
Thempublisher mmakes mno mrepresentation, mexpress mor mimplied, mwith mregard mto mthemaccuracy mof mthemi
nforma-
m tion mcontained min mthis mbook mand mcannotmacceptmany mlegalmresponsibility mor mliability mfor many merror
s mor m omissions mthatmmay mbemmade.
Printed m in m them United m States m of m America
12/3830/543210 m m Printed m on m acid-freem paper m m SPINm 10943403
, Preface
Probability mandmstatistics maremfascinatingmsubjects monmtheminterfacembetween
mmathematics mandm appliedmsciences m thatmhelpmus munders tandmandmsolvempra
ctical mproblems. mWembelievem thatmyou, mby mlearningmhowmstochastic mmethods
mcomemaboutmandmwhy mthey mwork, mwill mbemablemtomunders tandmthemmeaning
mofmstatistical mstatements mas m well mas mjudgemthemquality mofmtheirmcontent, mwh
enmfacingmsuchmprobl ems monmyourmown. mOurmphilosophy mis monemofmhowm and
mwhy:minsteadmofmjus tmpresentingmstochas tic mmethods mas mcookbook mrecipes, m
wemprefermtomexplainmthemprinciples mbehi ndm them.
Inmthis mbookmyoumwill mfindmthembasics mofmprobability mtheory mandmstatistics. mI
nmaddi tion, m therem arem s everal mtopics m thatm gom somewhatmbeyondm them basi
cs m butmthatmoughtmtombempresentminmanmintroductory mcourse:msimulation, mthe
mPoissonmprocess, mthemlawmofmlargem numbers, mandmthemcentral mlimitmtheorem.
mComputers mhavembroughtmmany mchanges m inmstatistics. mInmparticul ar, m thembo
otstrapmhas mearnedmits mplace. mItmprovides mthempossibility mtomderivemconfiden
cemintervals mandmperformmtes ts mofmhypothes es mwheremtradi tional m(normal map
proximationmormlargemsample)mmethods mareminappropri ate. mItmis mammodernmu
seful mtool monemshouldmlearnmabout, mwembelieve.
Examples mandmdatas ets minmthis mbookmaremmostly mfrommreal-
lifemsituations, matm leastmthatmis mwhatmwemlookedmforminmillustrations mofmthem
material.mAnybody mwhomhas minspectedmdatasets mwithmthempurposemofmusingmt
hemmas melementary mexamples mknows mthatmthis mis mhard:monmthemonemhand, my
oumdomnotmwantmtomboldly mstatemassumptions mthatmaremclearly mnotmsatisfied;m
onmthemothermhand, mlongmexplanations mconcerningmsidem issues mdistractmfromm
them mainm points. m Wem hopemthatmwemfoundm amgoodmmiddlemway.
Amfirstmcourseminmcalculus mis mneededmas mamprerequisitemformthis mbook. mInmad
ditionmtomhigh-
school malgebra, msomeminfinitemseri es maremusedm(exponential, mgeometric). mInte
grationmandmdifferenti ationm aremthemmostmimportantmskills,mmainly mconcern-
mingmonemvariablem(themexceptions, mtwomdimensional mintegrals, maremencounter
edminmChapters m 9–
11). m Althoughm them mathematics m is m keptm tom am minimum,m wem strived
