Schaum's outline of theory and problems of introduction to probability and statistics

378 Pages·2011·6.18 MB·English

by  Lipschutz, Seymour;Schiller, John J

SCHAUM'S
ouTli
nes
INTROOTUOC TION
PROBABAINLOI TY
STATISTICS
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Covearlpslr obabfiulnidtaym entals
Statiwsittilhca st aepsptc laitions
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Perfaeicfdto bre tter
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Uswei tthhce osuer ri!sI enlsr:lo Podr uocblaainSbodlin al liri!il Psyrol biacsb ility
ri!S lalri!i Isnllirocsd Sulcalliiosnl ics
10

SCHAUM'SO UTLINE OF
THEORY PROBLEMS
AND
of
INTRODUCTITOON PROBABILITY
ANDS TATISTICS
•
SEYMOUR LIPSCHUTZP,h .D.
PreoslsMoatrh ecmsa ti
1
Te0mUpinlvee rsity
JOHN J. SCHILLER, Jr., Ph.D.
AssoceisastMoaetr h Pecrmsoa lti
1
TemUpin0lvee rsity
•
SCHAUM'SO UTLINES ERIES
NweY rokS aFnar ncWiassMchcgGiRotADn o W.n. -CA, HcuI LkLl BaongdCo atráa Lciassb on
LoonnMd aiddrM exiCciotM Uya Mno ntNrweeD aell hi
SaJnu aSnip nogrSadeyn eTyo kTyrooo nto
SEYMOURL lPSCI-IUTwZh,oi psr eseotthlmeya themfacatuilcotsfy
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TempUlnei verforsmietrytl,ay u gahttt hP eo lyteIcnhsntiictB ruotoek loyfn
anwda vsi siptrionfgei snts hoCero mpuStceire Dnecpea rtomfBe rnoto klyn
ColleHgeer .cc cihveiPdsh .iDn.1 96a0tt hCeo urIannst titMuatteh ­of
ematSicciaelon fcN eeswY orUkn iverSsoimtoeyfh . i ost hbeoro iknts h e
SchauOmu'tsl Sienreia ersBe e gI/iil/lL/igl /Aelagre bDrias;c rele Malhe­
mali2cnsed,d P.r;o babaioldi lLyi;n ear2 nedAd l.g ebra,
JOUNJ .S CI-lIttiEsaRn A ssocPiraotfeeo sfMs aotrh emaattT iemcpsl e
UniverHseir teyc.e ihviPeshd . aDtt. h Uen iveorfsP ientnsyy lvaanndi a
hapsu blirsehsede apracphei rnts h e areas soufr fRadicieesmsca,rn ent e
mathemaatnimdca st,h ematica1 hbaiasol lscooog ayu.t htoeHrxeiedt o s
finimtaet hemaptrcieaclsc,ua lncudas l,c ulus.
Schaunl'Osu tlionfeT heorayn dP robleomfs
INTRODUCfION TO PROBABlUTY AND STATISTICS
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A Diviosi{oThenM cGraw-HComiIlpa nies
Preface
Probaabnisdlt lsialctttsay p peexaprl oiric miptlliiynmc aintdyli ys ecsip,l in
inclcuodmipnaugnt deo rri mnafstciiopenhn ycseci,hc esmg,ie sotlrboyig,oy l,o gy,
medipcsiynceh,so olcoigoyl,o gy,e dpuooclnaei,tct ioincoabmluie scssisscn,,i e nce,
operraetsieoaannarsdlc b lhr ,a nocefhn egsi neering.
Thpeu rptohsbieos io otksfpo r easnie nnttr otdpour citniaconimndpe Itehso ds
ofp robbialainstdty a twihsiwtcoihucb lsed uults oae lifln disvr iedguaaorlfd less
thfeiierol fsd pse ciaIlitids ze astiigonne.da s ufepomprel tnuoats l el acsu rrent
standaorrd a a tste exxttsbb,eo goikcn oniuinirn pnsgra e o baabnsidtl aittiys tics
withs chhiaoglohgl ae tsbh roean plrye requisite.
Thmea teirdsii avlii ndttewodo spianrtcthleseo , g diecvaell ionspo mte nt
distbuyrt bhdeeid v isiouns uenwlfehsislat e e aaxtsnth d ee rreebnfocoieks
increased.
Parcto vdeerssc srtiapttaiinesvdlte ei mocepfsnr tosb aTbhifeli icrthsyat.p ter
1
tredaetssc rsitpattwiihvsietmc iohct si vatecso ncvaeapprptiesoai unrts ih neg
chapotnpe rrosb aabnidl sitethcyceo,h n adpc toevsree rtssc onautnidn g which
are nfeoaer d meodd erno ft rapebraiotlPbmiaetranytlt. is noc lau dcehsa pter
1
onr andvoamr iabldeesf eiwxnhpeee rcveta arwtieia onsnct,ea ,nd deaavrnidda tion
orfa ndvoamr iaanbdl ewshd,ei rsaecn updwsr esoC vhee byisnheeqvau'nasdl itthye
laowlf a rgee rnsTuh.imi fsbslo lobwyae ds ecphaaropanttt ehebre i nomial and
nordmiaslt ornwishb,eu rtceie ntlthiretma hilet o irdsei ms ciutnsh cseoe ndot fe xt
the naoprpmraolxt iom atthieod nib sitnroimbiuatli on.
ParItIt reiaentrfse nsttiaatlIi stbt eigwciisnta.sch h apotnse arm pling
distrfiobsrua tmipwolinitsnh gw iatnhrdoe uptl aacnefdmo sermn aatln llda rge
sampTlheetsnh. ea rrceeh apotnee srtsi (mcaotnifoiinnd teeanrncvhdeay lpso)t h­
estiessf toaisr ni gnp golpeu laantdi otsnhe,ep nac rhaaa ctpoetv eertr hiensge topics
fotrwp oo pulaLtaistothnleisyars.,c e h aopntc ehri -tseqasuntaadsrn ea loyfs is
vanance.
Each cbheagwpiitncteslhr es atra teomfpe enrttdsie nfeoinnnptsir ,ti incipIes,
antdh eotroegmewsti hitehlr l usatnordta hteirv e dmeastcerTrihipiiatssli .v e
flolobwye d grsaeodtfess d o lavnesddu pplepmreomnbstlaT.erh ye solved
probsleermvisel ltuaosn atdmr patlthieef y maantpder roivairlde,ep etothfie t ion
bapsriicn scvoii ptIeaefflse cltteoia vren isnugp.p leTpmhreeon btlaermys serve as
ac omprleevotitfeeh mwea teirni cathlha ep ter.
Wew itsoth h amnaknf iyre nadncsdo llfeoarg uienssv uaglgueaasnbtdli eo ns
crirteivcoiatfelh mw ea nuscWreai lpstot. eo wx ipsorhueg rsr sa ttitoth suetd aeff
ofM cGrawp-aHritlitlcoB,u a lrabGrailrlyaas n oMdna rLyo eGbiislgf,e o trh eir
excecloloepnetr ation.
SEYMOLUIRP SCHUTZ
JOHJN.S CHILLER
TemUpinlvee rsity
111

Contents
PARTI DescriSpttaitvieas ntPdir cosh ahility
ChapterP RELlMINDAERSYC:IR PTlSVTEA TlST.l.CS. . . . ... .1. . . . . . .
1 1.I1n trod1u2.Fc rteiqounTe.an bHcliye sst,o g1r.Ma3em ass.ou fr es
CentTreanld eMnecaaynn: Md e di1a4.nM .e asoufrD eiss persion:
VariaannSdct ea nDdeavrida 1t.Mi5eo ans.ou fr ePso Qsuiatritoinl:e s
and Pielre1c6s.Me .en atsoufCr oemsp aSrtiasnoUdnna:iar tndCsd o ­
efficoiVfeanrti a1t.Ai7dod ni.tD ieosncarolif pDtai1t8o.Ba ni.sv ariate
DatSac,ap tltoe1t9r.sC .o rreCloaetffiico1in0.eM n1ett.h oofLd esa st
SquaRreegssrs,eiL oinnCe u,rF viet ting.
ChapterS ETASN DC OUNTlN.G. . . . . . . . . . . . . .. .4.5. . . . . . . . . . . . . . . .
2 21.I ntrod2u.Sc2et atinsoEd nl .e smSe,un btsets.D iam2gs.r.3a Venn
2.S4e Otp era2t.iF5oin nsai.nt Cdeo untSaebt2ls.e.C6 o unting
ElemiennF tisnS iettes , InclPursiinoc2ni.-Pp7ErI xoecd.lu ucsti on
Set2s..C8 l asosfSe estP so,wS eertP sat,ri toi2n.sM9.a thematical
Induc2t1.iC0oo nu.nP triipnnIgce 2is1..F1 a ctoriaBli nNoomtiaatli on,
Coeffici21e.2nP etrsm.ou nts2a1..t3 Ci omboinnsa2.t. Ti1r4eD ei a­
grams.
ChapterB ASIPCR OBABILlTY 87
3 3.I1n trod3u.Sc2at miSpoplnaea.c n Eedv es3n..tA 3x ioomPfsr obabil­
it3y..F 4i nPirtoeb aSbpialc3ie.Its5ny.f SianmiSptpleae c 3e.Cs6l. a s­
siBciarlt hday3 .EP7xr poebclteamt.i on.
ChapterC ONDITlOPNRAOLB ABILAlNTDIY N DEPENDENCE 109
4 41.I ntroduction. 4.24 .F3Cio nnSidttioetc ihoansatli c Probability.
Proceasnds esDT iraeger 4a.mT4so .tP arlob bialaintdBy a yes'
Formu4l.Ia5n. d epEevnedne4tn.Ist6n. d epReenpdeeTanrttie adl s.
ChapterR ANDOM VARIA.B.LE.S. . . . . . . . . . . . .1.32. . . . . . . . . . . . . . . . .
5 5.I1n trod5u.c2t iRoVanan.rd ioam5b .Pl3re osb.a Dbirisiltbiuttyi on
oafF inRiatnedV oamr iabElxep.e cot5afaF. ti4in Roiantn edV oamr i-
abl5e.V.5a riaannSdct ea nDdeavrida 5t.Ji6oo inDn.irt si tbuotfi on
Random V5a.rI7in adbeplReeansnd.deV onamtr ia5b.Fl8ue nsc.t ions
oafR andVoamr ia5b.Dl9ice sr.Re atned Voamr iiaGnbe lnees5r .al1.0
ContiRnaunoduVosam r ia5b1.l1Ce usm.u lDaitsitvreFi ubnuct-ion
tio5n..C1 h2e bysIs nheeqvau'nadl LiattowhyfL e a rgmeb eNrus.
ChapterB INOMIAANLD NORMDAILS TRIBUT..l O N.S . . . . . . . . . . . . . . 180
6
6.I1n troduBcetrinoTonru.ilB alil6ins. o,D2m i isatlr i6b.Nu3ot ri-on.
maDli stribEuvtailounNa.ot rimP6nar.glo4 b ab6i.lN5io trimeasl.
Approxoiftm haBeti inooDnmi isatlr i6b.Pu6ot iisosno.n Distribution.
6.M7u ltinomial Distribution.
v
CONTENTS
VI
PART 11 InfereSnttaitails tics
ChapterS AMPLlDNIGS TRIBUTlONS 210
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 7.I1n trodSaumcptWliiiotnnhg: anRde pWliatch7eo.Smu2aet mn ptl.e
Mean7..S 3a mPprloep ortionV.a ri7a.n4c eS.a mple
ChapterC ONFIDEINNCTEE ARLVS F ORA SINGLPEO PULATlON 236
8 8.P1a ramaenStdte arsts.i sTt8hiNe.co 2t oifaoC no nfidence Interval.
8.C3o nfiIdnetnefcrroMev e aalns8s .C.4o nfiIdnetnefcroPevrr a olpso r­
tio8n.sC5.o nfiIdnetnefcrroVev a arlcisea sn.
ChapterH YPOTHESTEESS TFSO RA SINGLPEO PULATlON 261
9 9.I1n troduction:A bToPeuastrt aismn.e9g t.H e2yHr pyoptohtehseesse s
TesfrotM se an9s.H.3y potTheesfstoPesrrs o por9t.Hi4yo pnost.h eses
TesftoVsra reisa.n c
ChapterI NFERENFCOER TWPOOP ULATlONS 291
10 10C.o1n fiIdnetnefcroetvr haD eli sff eroefMn ecaen1 s0.H. y2p otheses
TesftotsrhD ei ffeorefMn ecaen1 s0.C. o3n fiIdnetnefcroeDvr iae fflrs­
encoefPs r opor1t0Hi.yo4pn ost.Th eesfstoDesris ff eroefn cPerso por­
tio1n0s..C5o n fiIdnetnecfreov Rraa ltsio ofVs a reisa1.n0 c.6
HypotTheesfstoResras t oiVfoa sr iances.
ChapterC HI-SQUTAERSET ASN DA NALYSOIFSV ARIANCE . . .3.2.2
. . . . .
11 1.1C1h qiu-aSGroeo dn-eFsist- 1o.T1fC2ehs qitu-.aS Treefs otEr q ual
Distri1b31uC .thiio-nSTsqe.ufs arotIr ned epAetntdresin.1bt 41u t.e
One-Wayo VfAa nrailay1n.s1Tc5iwes o. - Way oVAfna arliyasnicse .
APPENDIX 359
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
INDEX 367
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PART1 : DescripfSifvaef isfaincdPs r obabilify
Chapter 1
Preliminary: DesSctraitpitsitviec s
1.I1N TRODUCTlON
Statoint hsoetnh iea cnmsde,,al nisos nftu sm evrailefuaoeelrxs a;m tphsleae l,oa tfrh ieeem sp loy­
eeosfa e ompoartn hySe,A sTe ortehse oifn eomoifaun ngi vsetSrutsdaietatnisaytss .ste iieesn ee,
ont he hoatnihdtse,h rb e r aonmfea ht hematoiregsa anwnihazileaeysnhzi,d en st,es ruprerahew t s
datSat.a tmiestthiaoeradaepsl p ltioea anaybr loeefh a u meannd ewahveonrrue m eriaerael data
eollfeoserot mteeydo p dfee eisiopnr-omeaeksisn.g
Thpirse liemhianpsatiremyerp o lvye rsr elttaootgp eaidte hsae nrddie nsge rdiabetiaanl gl ed
Depstcirviset iISwctit sbla.eult s iiebndo tthhfe i rsottf h tpeea wxrhtti,m e ahi nlPyr otbraebaitlsi ty
Theoarntydh ,see epoanordtft h tee wxhti,me ahi nlIyne frterSnettaaittasil s ties.
Real Line R
Thneo taRtw iiboleunl s teodd e ntohtseeeo tfr e naulm bers, nwuhmibweeehur ssfaero r e the
numerieWaeal s msdeua rtteaha.eid f sea irml wiiattrhhg e r aprheiperaelso eRfn ast aptooiniao n nt s
strlaiiangpsehi ,te tiunr 1eFd-iW 1ge..r etfoseur a el hi anse r teUhaenol ert h ree UanRle.
-:n; -,[5 -,fi :n;
1 1 1 1
i i i 1 i i i i i ..
-4 -3 -2 - Threoe allein 2 3 4
R
Fig1.- 1
Frequweewn idtlell y a sle otwnfsiu tmhbe earlisln etsde .Sr pveeailffoairner yae nlaullmy b,ae rs
anbdw, i ath b w,ed enaontddee fiinntsefe orrmatv boaa l fslo lows:
<
(a=,{ b:x) x a b }o,pi ennt erval
< <
[a=,{ :xb ]a b ::}c:;,l oixns te::edr:; v al
[ba=),{ :x ab::}:;c, lx o siendt-eorpvaeln
<
(ba=],{ :x ba b ::}o:;e,p cn l-oinsteedr val
<
Thaeta ieinhst ,ee ornvosaafill slt st he apao nibdtn; htt ese "rbcmel toawsneedbed rn"aa aerkuees te d
tion ditehtaahteteen dpboeilntoton gitsnh teae nrtdvht aeel "r omp aennd"p aar enatruhese tesodi s
inditehaaantt e e ndpnoobiten ltto otndh gioe ne tse rval.
SubscNroitpatt ion, SySrnubrnornla tion
Consail dioesnfrtu medraitseaaat,ylh e woeefii ggshhtttus d enmtasay.lb ledT ehneobyty e:d
The nu12m,,b, ew8rrs i btetletonhww esa reea lsluebds Acnar ribpittsr.ai rtnyh l eiwe siltle lm ent
...
bed enobtye dT hseu bsjie esra ilaplntie ndbd eeexia gtui stvehe peso siottfih eoeln e mitneh net
lis(tT.h eWj i'al nekdta traeelr fsesroq ueunstaelisdyn dexo lssy.m)b
2 PRELIMIDNEACSRRYI:P TSITVAET ISTICS [CHA1P o
Thseu omtf h e weeiigoghtfhtht s est udmeabnyete sx priens fstoehrdem
W+¡W +2W +3W +4W +sW +6W +7W g
Cleatrhelixysp, r feostrsh ieo wnso uubmlev d e lroyan ngad w kwtaour sdie f thmearnemy o wreer e
numbietnrh lsei sMta.t hehmaadste ivcesl opedfr os au cshhw ohsriuitcimshhns a d nedpo etfnh dee nt
numboeifrt emsl iisnt .t he
Summantoitoaunts ieossn u tmhmesam ytbio(oltn Gh ree leekts tiegrmS ap)e.c igfiivceanl lay ,
¿
liXs,¡t, . X ,.n2Xo. nf n umbietsrsusm m,a byed enobtye d
n
or j=¡x ·
¿
J
whiicrshe ad:
Thseu omtf hxe- sjauss b-j forgmot eno1s . It fhe nnou ifmtbeieumsrns d erwsemt aosyoi dm ply
write
x
}
¿
More gseunpefproa(ilskasle)n ya ,l geebxrpariiecns vsoitlohvnvei a nrgik aa,bn nld¡ae n d2a rne
intefogwreh rinsc::¡ h:; . Tnh2ewned efine
n2
f(kf)() +n f =¡(¡ +n 1f)(¡ +n 2+ + ). +.f .(2) n
k¿n¡=
Thus wfeoe rxh aamvpel,e ,
g
w}= W +¡W 2+ W +3W +4W +sW +6W +7W g
¿}¡ =
s
2 2 2 2
k= +34 +5 =9 1++6 2 =55 0
¿k3 =
akbk= a ¡+ba b¡22+ . +.a n.bn
¿
¿(x)- .lx= ( x-¡. lx+ ( X2- .lx+ . +.( .nx- .lx
(Waes msetu he infdoremx t on1ig tnoh elesa sts utmwso. )
1.F2R EQUENTCAYB LEHSI,S TGORAMS
Onoetf h fei trhsiton nguess ualwliyat l hda orlegiosesnf tu medraiitcsaaf lot rsomo mteyo pfe
ferquteanwbchlyete rh,teea bslheot whnseu mber aonif n dtiiivmtieedsmu aoltc hceu rnosuf m obre r
itemsfa wltilht ahgtii nvi enant eTrhveafselrqe.u ednicsyt rmiabbyue pt iicotnuussr ihenidgs to­
graWmesi l.l usttercahtwneii ttqtwhuheo eix sa mples.
EXAMP1L1.E An apahrotums4een5a t ph aarst wmiettnhhftel os l,o nwuimnbogtef er nants:
2 3 5 2 2 22 4 34 2 6
2 4 34 4 2 4 4 2 2 3 4 2
3 5 2 43 24 4 2 53 4
Obsetrhtvahetoe n nluym bwehriascp hp ientah rle ia sr1te2, 3, 4 ,5, a ,n 6d. T hfeer quednicsyt roifb ution
thneusmeb aeprpsie Fnai r1gs2-. .S pecicfoilculamiltnsl htyles, n guimvbaeenncrd os l 2ug minv efesrq utehnec y