Soln_3 - E5600 IL/ameumré if 3 50(447‘IIH43 3 77610061” 2'10 7/oof[72;41c/¢¢r1£IJ —‘'7rwa for n=2 2 since 73(A/7A7)= 7(AZIA)7D(A 0 Now

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Unformatted text preview: E5600 IL/ameumré if 3 50(447‘IIH43 3. 77610061”: 2'10: 7/oof [72/ ;41c/¢¢r1£IJ-';. —‘ '7rwa for n=2_ 2 since. 73(A,/7A7_)= 7(AZIA,)7D(A.). 0 Now Sula/pose H: five for “era/n. We Musf slaw [+5 +IUL£ war #74! as we // (me/“4a., 549/2) ’P(Am,nA,,nv~/)A,) = PIAMJAnnmnA»Pawn-0A.) = WANmnnm/m.» P (AnlAn_,fl--vfl;4, )thg ~ I n A.) l . ,' I I gnaw/An n...nA‘)P(AnIAM n. . . An”. . .. ‘PIAZIAJPMJ .50 We Concludle If is -l/ e +1, 74;} 4‘8 Proa‘f [LthLf'l‘OvA‘d Jar n C0“? 2. ’Parouc/ls 23"“: The 7‘04a/ M.ch Let 0-; Subre‘fs our/LI _.———n_. M elememts 1.5 7/12 45 ‘la/ number" 07(- M éIIWefl+ suLSe'ls (on4a¢‘n{m7 J: [‘5 (SU‘); 14;: is Lerause. luau/2:7 ‘ J; "5 "’ 742 SuLSE'I‘JYOu can sel-efllc 44¢ (PMat.wt‘l7 m—I ekmcea‘fs of 742 subse‘t‘ from 7417 femfiifll‘v M-I elevated: in (3;!) ways. If «Cacti m ~€I~€meac+ SuLxef 3"" I;/<e//‘5.1h.eq 'Hag Probub2[¢'¢y P of selec’flv one UHF/1" fa “" ' ‘5 no. wq 5‘ {0 {CL n—( (01-0., [-7 = (subsctywdla g: ) z ("I") = (mvl).'(h-l-M-HJ.‘ o-Ig-I-EI no. out 5 +0 n h! ( Pick SQLseyf: ) (VI-1H m! = __.___ _. L”. n! m4)! n 19.2. 3. 'Pa cull's 2-17.: "A'f random”: All when: t owl/7r likely. a. P 7 , ( #1 =3 Prob. of roll :3: on}! +foue "Mel-Ia] rforor‘lflun.’ +0 m4!qu I“: a can 'P(i6$t$83) -.- __...’3-6’ = Z; = [95—] _ "0‘0! Io (bYHiést 5 5312-1953) -.- “Hicstsssnitwfl Pli£>53) =W-L§;fl_z -—- Haws) _ Ito—5’! 5 _.—— i?drekll-S 2",3: #L'Ie 4:05:29) auJ We will assume. +5! Probe-lain“, ff cum-{s is sfeé‘fiéc/ In] a [.2ch silt)- “Wm-s we hat/L 7(i'ta'5tst04-t’3lit ;£03)=. i£o<tst {vats/I is“: 7(it2-1563) I am J1:— := 4;. ___......._° and = dilihil'é Lwdlfklt ) ' J Ezmflb -+¢.do flakLs/i'lféJ‘L, hrpafllosi: ), we Law?— Ali) 4!:- £1 J; =qut)d£— ______ 0") I“; it} alt o to M “‘“54 5‘1"” 0") 7Q!” GUY)- we. do flu-.5 507171147 itr—‘At , dc‘uc‘JL-«j law/h sic/es Ly At, auc/ 1941917 Ai-PO: t +at LHSUH: Jul- z'gLSzcht £4.90 a = 23:0 j—t[Aa,+ot)—Mm] £50qu W =_°i(i.tL—— . Here Alf) is vb. nd)_ It) Alco)‘AH-¢) aufidemldwe of out} 3 at: ~43! . at eusm: fidu’ =-~= ‘ ' 4“ mm: 4 a) owéo) =.- (d Aha—M5) d L— (H) O Eyua‘hztb LHSG‘) anc/ RHST“), we 7e£ 7.3 (‘4 -~ (onflmuec’) .70 o((-f) flaw (59"), We ;‘44e7"i4€- Len“: 5:079: (Unfit. "LO over ‘146 ln‘lffo’o/ (0ft). 1‘: 'AU‘fl'Al‘U 4,5450%): okHo) at = -fdu _ o Mad—Alia ° 7»? "I"[M°°)'mfl Afoo)~A(0) +}M[A(co)-A(o)] t puswk): [Guam-L, —_- wow: 0 gfua‘hij- LHS (H) «ml RHSM'H, we jet -_1« [A(Oo}—A(£)] +1” [Alger-14(0)] _— 4(o)t . job/[mi {or Ai‘é) AH) == (Acoo)-[Acoo)_Aco>]é°“°’t) 1 a) \—-——'y-—-———-—-J (0,60) 5.. #ke ,2ch db?) {5 K =. JAM _ 4mm: m OCH) At ._ cue) Ke. 10““) no M [Aec/uv fql-f)¢lfrl => K=1 . ° — ()t o. 9(a) = 4(0) 8“ O 1( (f) (ExfOueré/Iodrp) A f 91“) a“ i I ._ _a((o)t °< 'P(?_£-<t.3)=fotlf)clt = —e I= [*9 0 0 .5, il>0 . __S_o_ (Paroqjl-S 2’15: 7>rooot (VIC/“CHLqu W: £557 (cubicle-f“ 759. case 01". “=2 m), We. can purl"? A1: (A‘nAZ)U (A‘n 13-; 45) A __ ts om even . —r PIA.) : P(AlnA1)+P(A,/)A2_) J 3;” "PW/1K.) = P(A.)-P(A,/JA,_) Now ensue-Mt}? Al maul/LL S‘v‘q‘h Inc/(’0. (A‘J-LAz), le-I-s eke.ch A, awe, AL, 724 (5- (0M4ane4) ’Pm'nzz) = 1:04.)- Pm'nAz) = PIA.) —P(A,)I’(A7_) = 'P(A,)[z—P(A,_)j =.- P04910642) 9?, (ml. ’4?“th 111a Second few/7‘ "’9 A: 4““! ’42-) . D:‘L&(1 M know are (kc/elm (/14, awn/A; “’9 1"”!er yucl<15 I‘ll KL er-lktrmara ) .J. ('5 lude’gguc/en‘f of an, A J befiflufe. AIMS. =A anal 3} '—A;'r -’ = P(A)‘T(-3-)- .. ALLA, K‘JiAIJLIALHXL/Z; «Milli. F5" 39"“?! n ) We. assume 14,,“ Is ludéféuOI-éd‘lc op Alp”) An . 171‘- {a [/ows l'mm-ec/LZVZ-e& 74-27L h—q AyH,’ An+l lVlde-Pacb‘tf 036 Bl ) “'I E") . “P(B,n~ men/mm) = ’P(B,n~-/l BAHAMA “Pam-an Bnn m) :P(B,/l-~/H3,.) PMT‘“) ‘F (Bm-un Bfln A ) : Pas/run 507124 ‘$ 73‘ ) B7. ) t '0 ’ Br), Bn+l die ILLJPP- é;- ’?c‘r°“(“-5 Z‘Ie: 7kg "Rm ‘er a"! o/cs‘flnc'ic 524‘: 0-.F 5M o‘jef/S ‘14e7‘ (an be Se/ecvl-aalarfom n OEJG‘JS ‘5 5.9 '1th axe Possc'Lfe Combinq+t'oo1,5 of m eaevzfi “(1‘42 {Al/och firfl we M41454 (heck: 7(Ad'lfl-“0A5m) =?(AJI) Jammy, we. I'M-‘5‘!" Check-75.55 {5r m: 2)?J .n)", 7h“5 "there are N: (g)+.-t ) e?mS.-I*o c‘lQLL. In 31%ke bMoMfiz/‘f/tmlem m n-m 2"=(HI)"=Z7(2)1 1’ (hf—‘0 (g, - coachuma 4) = (2>+<2>+~= “NW-5 ‘7‘ {slaw-’5 “it“‘fd N: Zn—(n-H). .——_ (A : —/ (‘4 t.” (1' = Laws :Dea‘me. */ ha CVPVNLS arrida/ #:‘me 4‘“ annual "I’l'me 'La {I'LLCOO A: 4n“): q/ru/CS In rn¥€’l’¢¢{ “Wig—1)- B : LUIS affl‘VES (:4 (“‘{elt/ql (1523,14) 7>m= +z—t' “a m)= tarts. 60 ea anPFemJence a)“ ar/(a’q/Vlmes 1w #421, In —F(A/H33 = P(A5P(B) : (£2*tl)(‘£q-t3) M 602- E” #‘Le. 4IQL‘A and 4&0. lat-LS 60 “+0 me¢+) M mus‘f' be less 7'qu (Ti-K and u— MM+ be @55 ‘féfll‘v (44-10- L-efs‘ Ce[/%;S euem‘ D. (0 =9; :D= Z—tosu—vsxg 5° 3) COIFQSfJade -/-o ‘ike rejcén :7. q>d¢f30ull.5‘ '2"? 5 (See. EXam’ale 2' [Bu—l.“ quou/trs) Made up o-P film We *ch’oe'aolis wn‘h 4.0215 A. (AA Ali u .a = A +A’ Z ) l 1; = (lO+X)60-10 -352 - 6° ?(D) (,0;th 72‘ «ad So[ULt:‘7 in L K \ll-Q {Ll X:- éo—IDVH . 7.6 3—. (Paraglcs 2" 2.01 ?roo1£ inc/uc‘lio'v‘ Obnowstf "frat. {5r [<3]. We mac's" 54.4w M1: -. 4 1:5 6:42: ‘HqfiL )‘ Jar k-l-l- (cub. c/eqt{7‘+fmc~p:r I<=l becawSL‘f‘Q) "OHM—Le" a; oa-P. elemen¥faé;.£r 1:; n " 0:42 [or anal! .ef-t’meac u If (4' Is +fuc€ firmycuedal 1:. N,,ua= M = k:(9\'l<)'. [.1-..K 39L 4‘12. ‘lwdwc4l‘old 54? , we M4ch 54,094 “7144+ “‘1: Nn {k+l)=Nn(/<)- Mk“ ) I<l¢<n - .I-F out a'H-cnclt 4n cecal: /<~-e/«emeo¢1" Subse‘ital’s Obie QJJC‘FCBKQI {lemma-.4 -- page 0-; 7'42 Ida-Hitbt‘? H'lc element-45 0‘; S -— WC ‘féeu firm Nn(/<)(Vl——I<) k+l f/{weygf SabSe'ILS , flawed-€12) 744312 51463374.? are my; (all, C(Lkv‘Ihnd‘, 742?; £19“ ire:qu eqcéoae “Jim-.24 kqs k‘“ h/mfi'ée/ suéfe'éf #:«ce Nnuat) = Nn(/<)- ""< I<+l l (quOu/l‘s 3" 5 BeiKOu/i .7Il-QIS :z-F A = {Sex/en} ’PG-Kocculs {0 +cue53)= : (—5—)!0 (p 7) =7 I” area]: 10 fl’meJ} ) = 1-03)”. 7.? Q; ’Pafoulls 3’2: Lei K be ifienuméer of "head/5” 1;! n 6““ +0539:- Let E":- 142 numézr a~F Zeno/5” I.» n 40-5575 IS an even “IMMLPF. 71,90 En:{ Zk=03UElc:ZZU---U{k=n3 , new-4; §k=aguzk:23U---Uik:n~l§) n thl. ‘Tlms we. have. ’P(En) = {Wk303)+?(z’€=23)+"'+P(ZI;:I)3) ’ n {my}; 7"§k=03+PGI<=Z§+m+'P(§/<=n~:3), n UJJ. So we huue- ‘f‘uu'l' 7(2..)= 3" +(2)r13”'1+(g),043"-‘g . n —- ~—1 Ira-k " L (31);»? k=o haven “if 1= (1%)": E” f?)rzr""+(2)r%"'3 " '+ (3)?” (WW 2:"-(.")Pz”"+ (2)172"? -- - r (2)?" flint; 4000 .ef/bregsraacs) we )e't'" n '* ESL-W" = 2217(2)r“zr“"" = 2m” ‘RX -—_. H . cha’oou/lk 3" 3 1’ 7‘3 *“fi/ “o‘MLN‘ arc “JG/S 4a Se/ec‘; n oéd‘ec‘lj from N mug is (N) 71 TAC 401(4/ VZ°U4¢££P 6‘46 Ways +0 so 42+ [C oéd‘eozs {fem “Me K 960:! oéjfirfis 1:5 7L2 flak] number (9-K wan/s +9 ick h-k aéd‘ecfi‘ VQom “The. N-—K defen’a‘za oéJ‘EC‘Q is (N—K h-k Hence. +1.0. +o‘le{ [duméel‘ of Wat/S ‘fo /< .004 Cam/nousz Raf—J Vi-k defecI-iue Cam/Qantaw’éf ’5 ( K) (N-‘K l< n—k NOuJ because 4N Ways o-p céaarz}; 1’} about ecu)sz 700;...“ #[te +o~/Q/ of N (dW/Danénvlj are €7ua/é/ /f£e/y 3 :‘f‘ 7Q//0H/5 P ___.__ Nd. ways +6 k Zoacl «ac/flvk dflfec‘lflifl No. war/.5 1m rick n (owfoumvlj = (W933?) (N) VI ’2. ?a onus 3—8”,- [et A '3; k ‘48qu Show at“ firs'f H .— F +ossiwj3, Lu‘f‘ m+ Qualifier, B=§l<~l AGKJS‘ at n—/ fogsrkj g c: {he‘d/s .sIomJ: «75 n—‘fl- 54:37ij A 06?an {ff B/IC ace-«rs? A =73flc . ‘ .. _. _. n-l K4 n—k ., 'PKA)- P(3Ac)—P(r3)pcc), ?(B)—(K_I)p 3, > was? ’PIA3=(,Q:})PH32""‘-P = (12:11) Pkg-if Msflaawflwmi ____ _ , w, L; # _ Homewo rl< 3 50 {when A Jolene/um ( SOIu+t3AI ~10 44‘ Selma". P/o‘lom: ) i: ’Pafiou/l; LIOJ.I nob/Om Z—(é E ,3 2 5:4 or all ou‘lcouos of k sclcc-lelfioom n, (rower‘ 52*). 'L‘ '-’ , '3': ‘P: 01¢$$ttu//Id‘- measure $ Pun : [Al ‘JAéI 3 lfiJ . , J we 5 40 air“ k (a) {M I: 7‘9 Iain!- = (1:1,: Sati-fka'f M iswla’i'fii) bql’ JIQW‘ 7-04“! “KMLQI or MIG J~ +o JIaW [<- 54”! 10"“ ") m”) (wt-IN _ .51.... = (k—IH (on—k)! _ (ma)! k (wk)! ~ (“3 _ .____n_‘o _ n‘, (on—k)! “ k! (n-k)! m-l) : k” , a S k S M s n (") k 0 ) 4(SQIJL.<I~¢, ‘ no. of way: +0 (2461' k bat/S) ’aryesf’ (oqu )_ fuel} fik‘d‘ («I754 IS 5 M chm ‘< M (7041M no. up u»; 5‘ +6 draw k b“ is M m'. l _ I = _ ktCM-k)l .- M. (n ’Ofikfm n _ "I. — (K) k! (n44! 0 9!”th i FQFOu/I‘l‘ 41‘ PPOLIQM 2-1? Box (60:49:91: M “9“an hall}. [C Lit/{S are. H LlacL drawn from a 49-h! .l‘ m+h balrs. W4 wean" 7‘0 Fro‘oa‘azli'lr why-e [7 q)‘ [0&5‘)‘ axe w‘n’o lull Let fig k ball-f solute/ca, at? black Wag ai- lees'l‘ 94¢ (.5 wluye. 7km 13(W)=l—P(-M7)= 1- W5) 51°. or Ways +9 (Loosc k bull} = Suck 7La+ all ale black 70"“! no. of “fin/.5 1‘0 50(ec‘l k balls ) <2) z k! (n-k)! (ha-M) 0”“)! K k!(n+m~k)! = n'. (rum-(<3! (FHA! (an-HM)! ?(w\ = 1— "D __ MUHW-kfl (“1" (mid! (mu WWW-FMmmighwmmaM.WWWMNWWLWWWWL ?' 7" Ploblem 1’10 h CORScJ'Cr 'Ilte ruleJ Srual‘c :51 w/n'cln 71m cod/er op T52 at“) is Sal/cl. . for ~1£e enny +0 lie flag-Int] In 710 :7uarg, ,4; (on/r mus} It? I." ‘f‘c sLaolefi/rejloq ~60?" véu‘ fie (Irv/(l of ,5! ,N‘M/ 4“, “"4”! I‘D Q 1",,1 ‘55““f In '71“ s7uqre. ale equ/lf a: if! foxy/‘0‘! of 1h? (tau) (en/er, 224‘ we alarm! A g Fennr r3 PflJ’./0// (K $7qa/0. f: (95"fo or flan] (.5 In séalc/onnflfl 7‘94 ’P(A\ :- A’e‘i oIquJu/ "In; : 2!,— 5. Alex of 1” 97mm? “’— i’/' 1 I '//6 If“ , I m" lé (I 0 II al— .— 1L PaFoulc'S 4:4” PlotIOM 3" Let HR = A occurs «4 lausf' k—hluu «a n f. 0.414(0ng A "’- 14 carat: 4rac'l/7 k fade: 1"; n refel4¥¢54J . (a\P(Ez)=”F(E1)=/’ P(A.UA.\ = ’-[?(A.,\+P(AJ] r "[ (NW-r)"+(HP'WP’H1 : [- (c—F)"— n? (1-70)”, m HEB) = 1— ME?) = I—P(AOUA.UAA = ' - [ <2 ) row 4 <7) (2) rill-r3"? nth-n '2— 4 i: I " (I‘f)n + n PU-f)” .. rzup’on‘L ; to La6(€ Pete‘s/«3 463.! Problem 3’2— ’7ch an 36 e7u£ Ou+Comef (‘1 1/19 (cl/(:17 of 9 [Mar of O’(£€.7‘?7 (0‘9 6 ' k:[)£¢c’6. ‘fhe firm (it/c) ’j: 1"." I 7k“? VJ¢ huge 536- Define 1‘: cucu'l A : dodle 5:): : Clearly P0“: : 3"; final- “itcf (3(z or Q («0‘ of J‘E‘e- New Camp‘s/(r 50 rolls of a fen} 3'3 d“? (genuu/h‘ +I¢a(>)-De-fm,é ER : doub‘Q 51.x 0604/! “16 /eq,,1‘ k — dual; '1?) -. n u ¢ ¢ .e moi/u l< - ’fch-QS- .c { 7033) = 1- mg) = 1- P( Boo/3.013;): t-[rwgmagmmg] = '- U?) (at-m 2372353 (5.0>(s'—6)'<§)“"+ (i°)(:)2(%2’)“‘ ] _ o ‘l - _. ,- (33%)5— sogg-éxgg) 1.225(§)2(}3—g )6; (mam? 11; PG 6‘4!“ qCJ., Prob/om 3—3 When a fat} of {on} deco ale folk/a ‘7“ Samft-Q arac¢ 0'3 i:i(j'k);j:lpu’6; Igzl’..a,63 2-; )1'3'36. '7‘! euewf- A?‘= cu‘lcowe Sums +9 set/01 = i(l,e),(2,s), (3,4),ccl.3), (5,743“) 3 hai Jrk aux/‘omes ’ “.0. [A1lz é '2 F = P(A?)= --—-—IA:H = i = -'—- . (54 36 6 ~/ 1; WC new firm 1&2 c¢m4¢“¢¢/ 4" Mumf“ 0F /6 f055€> of Tie ’64:} offs». .r JICP) We (an J47... 74¢ 4.2014 E}: A $2090! orCu/S alc [4-5% ’46: (:3 [0 ‘f‘v/ouu: and “the {deaf} B :- A 3-9de a (ca/3’ Rmc‘l/f A - {all-05‘ K ~ ’ "" ’0 14/090), It?” P‘s?) = ’“Pf§7)= I—P(B°)= I-(i°)|°°(z-r)‘° :’ l—(z-Ip)’°= I__(Zs’)m : ’_ 4763‘25 6046e¢76 = 0. 335?le La, Paton/‘1’ 444.. Problem 3"? Let Ar = r Sufcé‘SS‘OS I.» n 4r'm/r B“ 7" Surcosr on {—44 fin}, ‘Pm‘. IAr‘) = PC BinAr) = PUK, “3‘- 3mm) PUMA 13(A") = (CI! ) P"'U-r’"‘" ' P (‘3) P""*P)"’r -_- (n—u) (WIN r-l __ (r-|)'.(V\‘r)'. VI) n'. (r r‘,(r\-—r‘)l. ...
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This note was uploaded on 10/12/2011 for the course ECE 600 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Soln_3 - E5600 IL/ameumré if 3 50(447‘IIH43 3 77610061” 2'10 7/oof[72;41c/¢¢r1£IJ —‘'7rwa for n=2 2 since 73(A/7A7)= 7(AZIA)7D(A 0 Now

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