Table Of Content

USED PEARSON ALWAYSL EARNING TimS wartz Introdtuoc tion ProbaabniSdlt iattyi stics 201r4e visbiyMo .nL esperaUnnciev,e rosfVi itcyt oria Takefnr om: EssentoifPa rlosb ab&i Sltiattyi fsotErin cgsi ne&e Srcsi entists byR onaEl.Wd a lpoRlaey,m oHn.dM yerSsh,a rLo.nM yerasn,dK eyiYneg Probab&i Sltiatyt ifsotErin cgsi ne&e Srcsi entNiisntEtsdh,i tion byR onaEl.Wd a lpoRlaey,m oHn.dM yerSsh,a rLo.nM yerasn,dK eyiYneg CovAertr:I llusbtyrB altyitRohunes so. Takferno m: EssentoifPa rlosb ab&ilS ittatyi sftoiErcn sg ine&eS rcsi entists byR onaEl.Wd a lpoRlaey,m oHn.Md y erSsh,a rLo.Mn y erasn,Kd eyiYneg Copyr©i 2g0h1tb3 y P earEsdounc aItnico.n , UppSeard dRliev NeerwJ, e rs0e7y4 58 Probab&ilS ittayt isfotrEi ncgs ine&eS rcsi entNiistnEstd,h i tion byR onaEl.Wd a lpoRlaey,m oHn.Md y erSsh,a rLo.Mn y erasn,Kd e yiYneg Copyri2g0h1t22©0, 0 270,0 b2yP earEsdounc aItnico.n , PublibsyPh reedn Htailcle UppSeard dRliev NeerwJ, e rs0e7y4 58 Alrli grhetsse rvNeopd a.rto ft hbioso mka yb er eprodiunac nefydo ,ro mrb ya nmye anwsi,t hout permisisnwi rointf irnotgmh peu blisher. Thissp eceidailtp iuobnl iisnch oeodp erwaittPiheo anr Lseoanr nSionlgu tlons. Altlr ademsaerrvkimsca,er krse,g isttreardeedm aanrrdke sg,i ssteervriemcdae r kasrt eh per opoefrt y their reoswpneeacrntsadi r vuees ehde refioInrd entipfiucraptoiosonenls y . PearLseoanr nSionlgu t5i0o1Bn osy,l Ssttorne et9,0 0BS,ou sittMoeAn 0 ,2 116 AP earson Education Company www.pearsoned.com 151 6 000200010271890609 RD PEARSON ISB1N0 1:- 269-92963-1 ISB1N3 9:7 8-1-269-92963-9 Contents 1 Introduction 1 1.1 Cour Overvi w .. . . . . . . 2 1.2 Exampl of tati ti al Practic 3 1.2.1 ampl Surv y 4 1.2.2 Bu in 4 1.2.3 Agri ultur 4 1.2.4 M di in 5 1.2.5 port. .. 5 1.3 About th Author . 5 1.4 om Thank 6 1.5 Final Word . . . . 6 2 D criptiv Stati tic 7 2.1 Do plot ..... 2.2 Hi togram 9 2.3 Univariat um ri al Stati ti 1 3 2.3.1 M ur of Lo ation . 1 3 2.3.2 M ur 1 5 2.4 Boxplot 17 2.5 Pair d Data . . 17 2.5.1 atterplot 1 2.5.2 Corr lation Coeffi in t 20 2.6 2 2 Ill Iv Contents 3 Probability 27 3.F1r ame.w ork 2 7 3.S2e Tth e.o ry 2 3.T3h ree DeofifPn riotbiaobnisl ity 30 3.C4o nditional Probability. 3 4 3.4I.n1d ependence 3 6 3.S5o mCeo untRiunlge 40 3.E6x ample 4 2 3.E7x ercis 50 4 Discrete Distributions 55 4.R1a ndVoamr iable 5 5 4.E2x ptea tion 59 4.T3h eBi noDmiita rli bution 64 4.T4h Peo io nD it rib.u tion 67 4.4T.h1Pe o io nP roce 70 4.E5x r cei. .. . 7 2 5 Continuous Distributions 77 5.1 aCndEdfx spe ctfoarCt oinotni RnVu ou 79 5.1C.d1£ . . . . 79 5.1E.x2p ectation 0 5.T2h Neo rmDaitl r ib.u tion 1 5.2T.h1Ne o rmAaplp roxitmota htBeii onno mial 7 5.T3h Gea mmDait rib.u t.i o.n . . . . 90 5.3T.h1Ee x poneDnitt riiablu tion 91 5.J4o inDtilsyt rRiabuntdVeoadmr iable 93 5.S5t attiiac nstd h eDiirs tribution . 101 5.T6h Cee ntLriamTlih te orem . 104 5.E7x eir . e. ........ . . 10 Contents y 6 In£ rence: Single Sample 115 .6 1 E timation. ........ ... .. . . 1 16 6.1.1 The Normal and Large Sampl Case . 1 17 6.1.2 The Binomial C . 1 2 1 6.2 H poth i � ting . 1 2 2 6.3 Example . .. . . . 1 2 5 6.4 Mor on Hypothe i Te ting . 1 29 6.5 . 1 34 7 Inference: Two Sample 139 7.1 The ormal C . 1 39 7.2 The Larg ampl C . 145 7.3 The Binomial Ca . 147 7.4 Th Pair d C . 1 50 7.5 Exer i . 1 5 5 Ind x 159 App ndic Appendix A: Solution to Selected Exercises 163 Appendix B: Stati tical Tables 169 for STAT260 171 Appendix D: Stati tical Tables 347 Answ r to Odd- umb red on-Review Exercises 361 Chapt1e r Introduction The e courI! e notejj hav eb een developed to as_8 i st you in the understanding of a first cour e in probability and mathematical tatistics. Such courses rii .$ are notoriously difficult and have gained reputation as "killer" courses on � many university campu� e s . Despite the difficulty, such cour1- e$ are amongst the most useful cour s that a student ever takes. Having taken an intro � ductory cour e, a student i better prepared to read scientific papers, as e s 5 � 5 experimental methodologie , interpret graphical displays, comprehend opin B ion polls, etc. Overall, the �tu dent become sa better critical thinker in thi age of information. You may be wondering why thee cour e note were written. The pri i; fl mary reason i that ome SFU faculty members were outraged to find that iii li the previou textbook was Hing for $238 plu tax at the SFU Bookstore. � liitl .SI Furthermore, I think that you will find thes e relatively conci e cour e note 13 le!1 s overwhelming than an 80 0-page textbook. If you happen to find a miS -· take or typo in the cour e notes, please email ([email protected]). l:i Many of the difficulties that students experience with introductory course in probability and 8t ati.s ti cs a re two-fold. FirIi t , there are many new concepts that are introduced. Se ond, the� e. co ncepts tend to build on one another. Ii: Although the cour e u e ome mathematics, and in particular some calculus, i3 6 S& the focu i on statistic . !'J i, 8 1 l CHAPTERIntr od1ucti on with oafx tr aina dn A ppn dioxn tain manayd ditixoeinr a lI. ti realilmyp ortthaayntota u t mtp mano f th promb lt oh l py ogur p t hc our that m n arm ardk w itahnas tekrh ia vo luttihoaantr p rovdii dn p pn clix A.U nliokm texotkb t h olutairop nr n idnd t aitloh l po u thitnhkr opurgohb lienam tsr tuu drw ayA.n dt hr i war ownagay n d ar igwhatty o a ttepmrpotmb lT. h wrownagi t ora dt hq ut iaonnd thn i mmd ialtyr a dt h lutiWohnn y. o duo a tnd n tod elvo apf alr a litthyay to uun drt anhdi nwg 1 1T.h rigwhaty toa pproaap crhom b li o g ivi ta olfifodro tn o uorw nA.f rt giving ap robal egmo aotdt emtphnt rt ha odl utTihoini . t hb t twoa y 1a rnW.h eyno aur rea lltyuk iit uua lmloyr ffi nit o akd vi ' I from iontu rru otrao t re a ahsiit n ag.n H opf ulhl yw yi gl ly to u bak o nr ak q ui kl-iy r. t btr Tt hhiam nud dlionnog u orw nfo rh ou.r Ifo ua rl ookfoirnad gd itiporntaaie lp romb lj ut g olo ounra r lib.rT ahrr nio h ortoaftg x et booonki sn trtoodrpuyr obayba inldi tattii. 1.1C ourOsvee rview Th ouri <liviidn ttoh r omponnt w itahc cho mpnotnu bdi viddi nvtaor ihoaup r .c hAar p otr rp ontdo r ougthwlwoy ko f matr ial. Th firt omponoeftn ht o uri d criptive tati tic .I na n ut- ·, h1 1d pr ntiao ondf a t(ia t rhn umerical ' 'L org rapahlii)na w atyh amta ki t i trod igt dha tao.m t im w 11-pnrtd d atra avl p atrtnt haatrn ot obwvhni l oouo kaitn g thd atianr afowr mC.h aprt a 2d dr d ripttiavtt ii. Th ondc omponoeftn ht o uri probability theory whhi i 1.2Ex ampleosfS tatiPsrtiaccatli Jc e addreedis nC hapt3e,4ar ns5d . I nt hree waolr slsydt,e amrsre a rdeeltye r minisTthiaictst. ,h edyon oatl wraeypsr otdhuecmes eFloevrxe asm.pt lhee, samaem ouonffet r tialniwdza etrge irv teotn w doi ffesreeenwdtis pl rlo duce twpol aonfdt isff ehreeingtIh nats si.t ualtitikhoeiin sit ,us s etfodu elc ribe thvea riaitnti hhoeen i gbhyat t ochasotrpi rco babmielcihsatnEiivcse mn. whedne termiynt iesrnet xiicism tta ,yb ec onvetnomi oedntethl e pmr ob abilisFtoiercx aalmlpiylwf.ee k neawlo lft hdee taaiblotsuh tie n puttos tossai ncg(oe i.ng . s,ph ieni ogrfhpa tit sneu, r fcahcaer atcitceetsrc,iw. e) , migbheat btloep redtihoceut t coofhm eea odrts a ilsc oimnp sltyeth xei rns. Howevieitrs m orceo nvetnoii emnptla yyt hatthp er obaobfiahl eiatdy is1 /2I.nt hcio mpoonfet nhcteo uer,w eg aiand eepuenrd erstoafn ding thien tuniottiiovofepn r obability. Thet hiarnddfi naclo mponoeftn htce o urissstea t istical inference whiicashd drdeni C hapt6ae nr7ds. I nfereinwsch eam to spte optlhein k abowuhte snt atiissmt einctsi oSnteadt.i sticiaslt hpeir nofecroeef n ce learanbionaugp t o pulbaasteiodona n ampfrloem t hpeo pulaAttfii rosnt. thougthhtim,sa ys eelmi aknei mpsoi biasl tihtseya mpilsae s uebt o f thpeo pulaatnitdoh nea, m pluendic tosub leqd u idtieff efrroemnt thn eo n sampulneidtT sh.e rewfoerm eut, b ec areifnmu alk isntga teambenotust thpeo pulaatnitdoh nii,s w herep rtohbea btihleiofrtroyymC hapt3e,r s 4a nd5 rie levOaunrst t.a tementst hrpeeo gpaurldabiastneiogdon na sampalrnee o mta dwei t1h0 0c%e rtaIinnsttyte.ha eadyr q eu aluisfiiendg probabWiecl ointsyi.td aetri sticianlt hcieon nfteoerfxe tne cseta inmda tion hypothteessitfosir vn agr iporuosb abmioldiesltsi.c 12. ExamploefSs t atisPtriaccatli ce To gaionm ea pprecoifta htreie olne voafsn tcaet ipsrtaiccitantil hc r ee al worlledqt,u' isc dkecl ryis boemp er oblwehmessrt ea titshteihocrasamy la de ani mpaTchtec. o mmtohnr eaamdo ntag l olft hper obliestm hsat th ey invodlavteNa o.t teh anto noeft hqeu estpioeo dna sra en sweasr tehde 4 CHAPTER 1 Introduction .. di cu sion is merely intended to initiate statistical thinking". 1.2.S1a mplSeu rveys Prior to elections, polling agencie sample the electorate and deliver state ments such as "32.3% of the voter in Briti h Columbia± 4.2% upport the Liberal Party 19 times out of 20". There are a lot of statistical issue in volved in a problem of this sort. For example, how many people should be sampled? How should we sample people? Not everyone has a phone and not everyone has a fixed address. How do we interpret the statement? In particular, what does the "19 times out of 20' mean? Although statements like these are common my experience is that few people really understand what is being reported. 1.2.B2u siness I am sure that you have been on a flight where the airplane i overbooked. Naturally, the reason why this is done is that the airline doe not expect everyone to how up, and profits are maximized by filling all the eat . On the other hand, passengers who sacrifice their seat on a full flight mu t be compensated by the airline. Therefore an airline mu t predict how many people will not show up on a given flight. The problem of prediction is a statistical problem, and depends on many factors including booking patterns on previous flights, the destination and time of the flight and the capacity of the airplane. 1.2.A3g riculture Farmers are alway interested in increasing the yield of their crop . The re lationship between yield and sunshine, fertilizer, temperature, oil and pesti cides are no doubt relevant. Note that ome of the factor can be controlled while others can not be controlled. How do we spe ify the r lationship be tween yield and the factors? How do you experiment with different condition