stat511ch4slidespart5

stat511ch4slidespart5 - fl Tke Befl’tk Fro lomlot.ll.+...

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Unformatted text preview: fl Tke Befl’tk Fro lomlot.ll.+ DI‘S'f-rl‘b +l‘0 Z “L H ._ Some r.\/.‘S IA in+arva| [0’13we SH—fror‘r on +lfle E ' Xam — l he ._ E Pro 9 +' -( Produd’ +k¢+ is PPuJean 0 0L d‘e'mic‘kl —-Tke ‘ F"°[>OI'+|0V\ 0-? 0L Sckool' WL‘o PASS & Sfindarotizd e:¢:+%a(u+s .— ' FroPor‘l'lon 0'? a has i \‘s ' “K ‘ +n. + n. ween-Hui wI‘HA 0L cer+¢itx \JI‘WMSF.‘L W— +5 " Tke befl‘a cLiS'l‘rilo +' ‘ mode\ 'For- SULC—lx r.v."3”.m IS A ¥lemue Dfi‘pn : A ‘f HA 4 r.v. [was a LLJFK clfS‘i’r'I‘oufion or am 1 ‘f A. Be,+aL(oc) i'p H's Pulp is: -No+€3 The begin has Surfer'f' on [0,1] I? Ox r.v. Y o-F ‘ In 0—H“ r in m as SwFPor‘l‘ on Som wa Cu) {Efrle [c,&] 0-? gini'k; lemj'l'lq flame bL model 'ere, +rcms-Fbrwxecl rav ) 7*: ~ Wi+L\ 0L bola oQiS'l’rt'kud‘ion. —Tke bed-K FoL‘F is very Llexilala) ckanyn SAAka drama-Hal” 'gr vara'ous a auxA % vducs 1 Grttk 0-? 885‘“ (1)2) Grafl‘ o‘F Beh(0.5')0.5) GrOLIL o‘c Bd‘K (1,3) GraEL O'F 8641(337-3 -19 on?) +Le— Be+m(«)§) PM is -1¥ o<<P) me am (vs?) pH“ is *I‘F <><>f5J 'Hne Be+a(o<)f3>) Pal-F is _Tke Be+q(1’134is+r}‘ou+ion is SimPly q d;$+ril3u.+ior\. No‘l'C3 Tke. \QC‘TL UiS+SJ low-1' no'l‘ l‘n c‘oseA ‘erm. The momen‘f's on Ice ‘pounot direcl'ly: TkCOY‘OM (Be—h mefim ama' variancas: I‘F Y~ Edmczx) R33, Haen FT‘DO‘FI I _ h 0 v(¥)= Finding Bah Prokakill'+ies -wLe'n (x anal are {M'ers) ngIl'K kadomhcs Com Ina 'RLLHCl via. Aired” I‘ni‘ejr‘q'l'ion or via er grand"; (cshL‘iskeA :45an rqead‘ecl fu+€fimfion Far‘l‘sv: wkida is cg Sum o‘p Probain lf+ies . -—I—F o( camel 53 are mf’l‘ \no‘l’L {ficjersj we can use R +0 4M4 loch: FFoBaLilf'l‘fflS (see excumr‘es on Course LUQL Page). EXCLEB‘C. 1.: DL-Chng +1“; down‘l‘ime Pk'l'fl CLS 'er Fr°P°r+i°n D'F +imc 0L. MQCJAI‘IQG. is unalflr Y‘aFOLir. Suppose a chr‘y Froaluces Maw—Lines kaSe. clown-’rime rad-c follows A bdkcgjlg) cl 'lS‘h’i loud‘l‘on . —bqu,‘}' {S +\r\& o“: 'Hnt Aewn'l‘l‘me Wilt Y? -Fm. q rmmlofly sded‘d MQCLlI‘ne) wkad' Is He olowh+fm£ rd‘e. ? 'l/Qkad' i5 ‘Hne. Prokaloilf‘l‘y "HAOJI' cL randomly Sdfichxl mackiue I\S under rel-JAN less ‘l'lthn 5% o-C Hue 'Hme? -I'F mackines ac} inclcrendexl-ly) in q shrmm-i- 0-? 25' matLinfiSJ naked is 44x; PrDLQLilf-i-y .Hmf ad' 1015+ 3 have clown'l‘ime rq_+£s grader 'Hmtln L}. | 0 TakeLiske-p-F ’5 Theorem —-T]r\€ SEPQAO‘ 0-? 0L olis‘h‘ikufion may \oe characl'erizd L7 ei'err 5+5 variance. or H‘s sfinclmml Amid-ion; "An «Avqn‘H—‘Bfl o-F usinj -I-L\& Shnalttral oleviod’t'on i‘$ ~Hx¢L+ (HQ/q) 0— is men-surest in +Le Same win as +ke Y‘.V. *Tkis «Hows us +0 makt car-him f>ro¥a¥ih+7 sh-lmen‘l‘s iAVolvinj )4 and Q". Lemma (MM‘kOWS Ine'T'L-L‘Lll.+73f Laj- bd be; an nonnejod‘ive Y‘.V. Wi‘Hn Pal-P (or Pm‘p) £6.90) 00161 lei c; > 0 be & camshvd‘. Then [FOO‘F3 -l/Je. win Prove 'HM‘S in 'Hafi Confi‘nuous mse. Conslolex +ke sej' —Tke_ taboo-F is Similar in Hle diSC—rd‘e Case. Tkto rem (Tckfi‘sys Loo—F '5 : (—91" Y Be a. r.v. (ud‘inutnus er- aliscrck.) Wi'HA mean fit and. VQrifiant <5"- <00 . For 0mm, k > O ! EXQM2\€. 1: Suflmse house Prn'ces {n ma arm fillow a. Al‘s‘i'rilou‘i‘l'on wier mama $?3 000 anal S'l‘anclaw-J Javia‘l‘l'on $201000. Ldkad‘JI‘S a. lower bouncl For Hm fmloaLi‘r‘J-7 ‘H/tod‘ a; randomly selec-I'QJ. Price; is lee-hue“ $LIBJOOO GUAA *|L*3,OOO? Examtle. 2'- TakekysLL-F-F's 'quor'em juqrqn‘l‘ees "l'lrmd' all; r,v_ wi'Hn meat-n )4 anal Shnolmr-A olQVfad'I'ovx <5- win have PFOLALilH'y acl' lexs‘l‘ of \odwecn )4—16' and )1+2.<r. —FE>r cLiS'l‘rikuLHonS wi'Hn "mound-SLAfd" dcnsi-l-ies‘l SuC—L‘ 0L Fro‘oa‘niluo'l'y may Le. subS‘hLVd‘i‘LH‘f hut-38x +L‘qh lower Lacuna“ *In SQCHOK we flannel 'Haafl‘ i‘p 7~Gammm(5—)3)) Y FFOLQLili+7 o? anus wi-H‘in 2 shndmni clevim‘h'ons 0F i+s mean. "1'? Y~Poi$(6.25)) +L‘en ...
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This note was uploaded on 12/13/2011 for the course STAT 511 taught by Professor Hitchcock during the Fall '11 term at South Carolina.

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stat511ch4slidespart5 - fl Tke Befl’tk Fro lomlot.ll.+...

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