Chap_4_pp.18-30 - 18 Observe that ed =l‘ X+ Xz/zl-...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 18 Observe that ed =l‘ X+ Xz/zl- "' X73,- + w ' Tag‘oCs 52¢ch X[um-~- x+xz+x3* , as x<1 QCome’fvicploafis'u ‘n (l'$)=‘X'-‘2‘XZ"13'X3- '- 05)“! “Eldhx‘g sedgs I e; Nil-x] .tx+x2+x3 + -- ~J . =3 “ If ( Vaughan-A For 02141 = e‘“("”‘) 2. \- X 3 ‘ ){X * *2/2! 4/3! * :Pro ggs'xhon (9013900 Apme-For o. BKMmiol m.) H7 X. is a film-mid, r.v.. yiflx Paramehrs 04,912 Pm? PM m {F 90128. k<fi~7 we" 44? 37k ‘5' “(mam )2< 3“? K (K '2) - ' flK < N u) e (NEE)_[(\ a) 1 e 7} )9 (K1?) efim "‘ Observe \‘Nfi For (x) N \or a GM (2) K“ 5‘3an NF£<W ribofk fix: ‘cfi' X, rigkhkorfi siécs of E1. (23]!) go ploacxx I F Q-NP(N K'. t (B3 me Weld (\ H .;Thus when N is \ou'ac. PM o& a \a'momiul —P__ Who’r is fl): PIORL‘J "r | . 500 Peop‘le. emc cg .. on Jan. :1... a k. SA 3C Tne numkefvoi have “\e'w hrfixéacjs on \m‘fk pommd'crs (N,pl=( PM = ( slgoxé)?! _ ) “\OA' in 0. Co fixem wi“ ‘nafe. \a‘. O 500, '/3L 5) l 365 mg; n on" Peofle 'm J“he compmgjkck will 30“. :1. is (1 admin]. r.v. w—K 19 20 N: 500) : Nob?" N d - P L37 X. W 322.1 V . NP. “m X For k445i in: 1323“ \mVe Zl 22 The Vomson r-v. is Q a 300d {0! mono flaw-cal s.‘*uqhons 03 can “1 uphmeufim" at “me t=o 0nd kt N be G (N. which e%ua\s J«u: nun-Joe: of omrremes of 30m: wetfl’ which hike flag; on “k “ng” inhruol [0,11] . For emmflc (somehmcb we can cock wen? omM’) 3 surges: Ni ) 0 5 t < °° 93* bf :95 {he {anew KngAPropcr‘hcs (3.) Ni ossqu onlg non ncfluhve, (“can Yokes anA N. =0 (ii) consiAc “w. (v. Xi: t‘clefinré 05 / indep.£$\'a\imu _x't3lt* 5 Ntz- Nt; :ngmg - . - .-—.—— number of ocwrr'anes a mmod: whic\ ocuu in he Rnhmol (tut - ' . .3 1| . ' an me. mm: (1* Th?- PM‘F O‘F Xtut dc fans only on We. duration w » -- . ofi‘xe ip*‘erva\~3it3z;t:; aha [10+ 00 1:. mmH32 inclivfiuo“): (finis is «NR! “16 si'ghonora incremfits may) (iii ) Hug-“(NV- 1.) = 1M0“) u) 9mm; Ni“); om / mlkd fichgjfl when. A {s o. posmvc audits“ and fix: nohth. .. “smou ck" stands for onyjfiAm’hon His) 3 _._- [Em fl“) hao F- :O (fir unmet: fflfl’kz is 001)) thvcas «hhsmhih MU. (ma funcjfiou cf k when OPPf‘oQChLi ZUo fin’fct {Mal a mnéam yous: fora: ‘L‘ °° /, M g g A ranciom vor'mUu- N»‘ which sohsfim. «whom (ll-(m1 QLue Xs canal Q Paissgg or SKI-nigh. a Pgiggn gro€c5§. _ . __ __ Theorem m se‘uencc of: rand m v0 6 Us '?oisson From» a _ .. O v Q } The numb! 05' union‘s P(Nt=K)fl; (AU efl‘t—n ,'-i=o,t;z. .. (3) of Q . __-_.__ __R.|._._______._._..__. _ _ . For k may Nt {Segue} a msson}.§}l_'wi_+b§1ué.{n(>.t~). Pf' consulevfiuhm ;n\cml (o,t*At}on& 59m 3" up in‘h halo in’tcwoAs, one of \engfln ’t Fo\\owcd ‘3 one of \eng‘h At. ~u K—At HH{ 0 t HM Define Pkt’c) 2 P { Nt'K} “” owl pi k (13“?ka Pf Ntmfik' I ,Ntzi} (5) Le. , PK (fl = “3: Pro‘mkdi‘n K tom‘s OC/C'W‘JP *0 *3 t m: t GM {3 K “AfiAH’ “\e pvoLoLSHa fl“. numhre-m“ of Genuine}: in the. inhruo', (o. :H.At] “0“ k P{Nt*At-‘- = P‘lN‘hAtS K) Nt:dj PiNt=i} P‘i Ntt-A’c'N’fiK‘i ,Ntfli} .- = by properw- (w) Pink“) ) 'nd nden - __, _- =' 'inctfmcnb : P{N£*At N‘ KQHN‘ J PiNt‘Jj 51 properi (ti) . fin’fiono r3 N = P{ NM: “(1} incremen s 25 Thus PJ’K (tit? At) Atpenas on‘u on “3: Wk \‘ime dWfizrencg M: and no" onA-t aha MI, and We, can Wrfic ;_-_[ = I 4: can: 32?ch E3 53-018411..- ° "754’£.?_0(Af)__ W Camtininj 53$. C91&(‘U_ : - x51». + out! Po (5) Al: 2b If JVenom from E%. no) that / 5m“- ‘gg‘fio 02:” =0 :1 m - Q¢t+at)-R(U - - Pa , hm \- XPolt) (H/ at Wit-*0 At 1H6 genérfil soluhon of £3.01) is p0 (t )= c c'“ (:2) Recon 9. (a); P{N.=O}=l K 8:: C = 1 in 53- (121 and POM: 6'“: (W) New am“ we Hove defcrm'meé 9° (HE ?{N\;=°J’, lei’ us nex+ Aficrmmg pk (HE Pi N: = K} For K! L ConsiAer one; (1 am “We non-overlapping ln’mvok (0,1:1 aha (t, ’tfibt] . Then NuAt can onla quoL file. inhscr K in fig, fonowing Affirm" Nays. Wm: "h: be no arrivo\s 'm the 'm’m'vul (0,11 oncl K ouwok in “2 in*etva\ (t,t* At]; 1 er: “M3 he. one mfivd in (0,1) and K-l orr3vo\s in (t,t+Afl; e’tc. Thus We conwrfic pro Pet ‘ 1‘3.) PKu MHz H “tut 3“} = 32:, P“”“'“ ‘N‘gflflNfiU (IS) use 2145) \,=ng PHMtJPJ-(t) (lb) 27 [x-z . + 1 W K. this w\'\o\t."tfm is dé‘MAhh': no“: “.2 “-2 zero whcfiKél P - . .4 (wt, (*1 s )3 PM (At) sow) (\e/ "I; J-° awfizm‘crfi , m) 3 Mat) ['3 frond; [£85] 51,- Eswz) m C°"“"“‘“3‘U7 12L W 7ich *- -~ M) = fi£§flfidfl__+g @fl_fm(t)1§kfi \ At At +7” Kn (NI huh: I a, p. cm: h l-gfkmzl x- mu: ggflu). - (amt) - . . . k M: 1105:)... (20} scepapa’ry an] ' ._.__ 3491:1853). . _._ L .. ._\__._ i __ P. (At) = iAL'i-Q-IAEL‘"--- . Combining) E35. (191-(zklyisldz‘__.__: 0051:) Mt- mH-MH; fidfifi'ka’cwmmmmfififi At - .___._ Af "" (22) K21 $3.13! = 21:10 W : ->~me +>xpm(t) K21 (23) ‘50 we now have {he fluctth dfi‘férenjtia) tjouo“'non fir Pk(’c)= P{N£=Kj 431‘“ + 7km(t-)-)~pK-.(t)=o , K2! Ml By clued" sugauh‘WOn d’ \S eosah verlfg K -24: WW: F{Nt:Kj-=O‘tii+ ) Kzi is 15: Soluhon of E%. (2‘1) Q.E.D. ‘E M50 vecau (30(17): P{Nt=o}= 6'} (\‘H ' t- P‘M m = cu)“e-” - ~ k!’ . 7-? Cncomesnic R-V- (p) 3Q: num\oet o; indepmém\ Bunth ’(V§a\s unxfd Firs’t Success pm-F Pix=nk=(\-P)nfip , n=\,z,3’... BUG: ‘lp Var [X]: If... i,2. Nega’fiuc Binomid (hr) 3C: humkr o; 3n3€9mA¢fl\ Benton“; *fiob uh“! Y Successes are ouumm _ _... _..- __._.___._ pm? .‘. P8903“): (2:3)P-YU'PPJ) nzr',r'+\’..'. em;er floss 9d -. . _ ._ Indep. hick ,euc‘n (e5u\\it\% in on success wii‘n Pro‘o. P) are gerion‘MA. Whfi "s *ht.9rnb.-.o£ Y iumcsss ..__ _____... ‘06-“: m fingcs. . _ sob: - _ _ - __ Y successea w.“ occur ‘oefine mfaflutes H'f _ *‘m H“ success occus no 105*" ’(bau \‘he Y+m-L-h{aL-_ rmd 2 )9?“ P)“. is “so: Aesired Prob. n: - ——-—-—y-———— r Prob. “1* T mousse: 4mm“; was #GF “LNG um wha’k; - __, n—(N-m)si s min (mm) ~ Where i. is a non-M3. in’tcaer ...
View Full Document

This note was uploaded on 01/14/2011 for the course EECS 501 taught by Professor Tecszs.. during the Fall '08 term at University of Michigan.

Page1 / 13

Chap_4_pp.18-30 - 18 Observe that ed =l‘ X+ Xz/zl-...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online