AgaLqumenr- a 1 BFagnotize Fithogo nally Pi the pottow tg mar arn. A= [ae oe € 2% V9 oo € -g -4 6 -g - ven Ar 7 2 % [4 py ey ante ~a 1. hs “2 Since w=aT, the sven matty Hho shot P= pTap ae icimdt McHAIX HEN we have to The chosactefarte equatfon @ the

344-219-2,- 9 > ©) i p2t4 +349 aac pb ?©. => AEAK = 04 Ke Suny Follon ame uel we rota WA-atd aeFom © and (=> ei ia ee Repel 9GS-C-DCD 23 .-a-a) 7-4 SA eM XB ck. => EG, Xy=t5K, HQ 5K a) S ee et ee Ea ia m/s ’ put 26 in eqn (): ee 2 be ° eo uy a ee fa 5 x4 ae eee? fs-ci L ire a 158 -O1g-15=6 = 0.x) -2%g-%z= 0 — @ O14 — 19° = -91, toXg-Xg= 0 > ©) “Ey -Ag-13=0 => — X, -Xg-%wso —@ trom @) and GP Yu ° 3 send > fee = O- ED) ee a for %> = -at-)-EDI4) Peete 2 SS for v3= 2ED- (Do) 6-4 8-) gro Fy " dite fe7 let > kK D> Werk, M22 Kk XBaas oma] SRife- |. t22-1 , Zara put A= in cn) = 4: OS RS i x ‘6 Pe oh => a “; = ¥ Bae é-@ -) || joie ra ei cs =) -) 5-8} b% et =a ie L4aq ese aes 9 BS Ge harl-yen 2320) -cH)-> TAL) -2tg- 23 =O =) ~O -ay,-132 0 > (Ey - 21 - hy - 343 20 — | 6) Hs 28 =BDDE ieee Fig = man fe ] = 4-4+t0=0 E. pa. ol? 1a] vitdtezo 14, Le Xz axe Btiogonat Amelzzatton g these VectdR ose given by. uy , Ug= 4 , Haat x0 Neat UX Me LOOP = fF gh = (IOPO=Z, laghi =) PEP a [2] [re wipe’ ef} cise é[3] ag ={4 |- -a[? 3 eq ove Bola Epps, a[3 os P=[us, up uz] p-[% “Mm ona pra) Make 1G : “VG Ye. “Ke “Wee ke He We ie 6-2-4 Ya Me He Va he Ye Ye Ye 6 o-[% te ae Ve . Ye “Us. Hence. matt & b Atrogonably ag naligarle.bea = 2. Eeploin 4ne following - ay Testing @ Htypotheida Baltenative Hypothesis — c> level g Sfanisftance yu») a) Teating 6, Hyphae Hypotiesia To neach dectefons akout population on the bata G Simple | Thpbmation , “e Make Cetaly asGumpttem’ about the populedfon Such astumptte fekich may 8 may wot be true ce Called reyportents Cstattetfcal Ky potheata) Null Hypothests —the hypetieati, jfimulcded sh the prpake g its aepectfon under the a&umpHon that HTS tue ta called the mull agpothest and Tt a denoted by Hy By atterate Rypothorts - Ang hypether?a mktch te Compltmentany 40 Hhemull Ryprthete 1% Called alternate hy pothoxds and is dencted by HI Type 4 ernb - FE a hypoterfs th hefected while if Bhould have been accepted Fg Gale Type ard Tyra oad . 4 a hypotherte te accepted while ft whoukl have been aefocted: TA called Wypes enh Cy hove ot stint ff cance The prooability level eelow which we ‘efect the haypothost& 78 Called cance Level rat we have St A 47 tevel g, Sani cance Bie | a \e 1.96 | ass Stteva. 9, Sip yf cance \ 41. tewel g Stgnigfcante bee, \ nese Nt} —PACKE 2 4.9883 ° in % he =“ atau) oe ssa s530] = +e a € 7 ze a3 tly = 3.958 é Sa fas Wis (2y> J aftes- ise) * 23 tly 6 -gi -; s*) Fo wiaes? “> Fries a a Ea, 21.2105 unde He» iy oh R48 Atsd. Los, from the Fodigtal b utfon table S02 0.08 Foes) (=? Vor) 23.89 i.e, raters 38> pe Md ee tration. Fear YtUTY =1R Sun of att ebscwatiom in dace Sampler Ta bmit Ste FS ts3= Sotuotse=120 cérectton pasa Ccr)= 12 = CPd>= 120x126 =1200 ” 18 ao. Total gum g te squcces set = (Ex!) tHe) VE xs)- CF $slc bbo+ U3242uU4- 1am = 1336- lRe0 = (Be BsTR= Sum g squmes berneen he sampler geste: [ (Bap a(em)* a 2 or + wo, o>" | 4 fee eee) sere Re USER +hboo +400 -1200 = gastumtaas-200 =50-1200 = 58) esTRe > Sia ieSsE=nithin the Samples Ssi-SSTR=136-50> 86 pefee g Freedom(Dt): dfy=A-1- 3-4-2 dfy> n-h- 12-324 MsTR= Betdeen the Samplas SSTR = 50-95 Begin 3 Mse- SSE = 26 — a SoS ae saa c ANOVA Table: Unde Ho: ‘Sous. (e 9 Vabtton Sum of Squeaes + Betheen Sample 5° «Foti? Samples 86 Total Faom the Fo ron table (Foes)? = Gonttusion : Fal Pt. Los 2. Wo t& aceopte ef. los Hence We concunde | a Commodity tn Hace 2 Th No Agni sel défperences nthe praces g 5. Saceibe one dime one Simeratonal “Teena mn, Taanape mm 1.192 dexine “rd at 9 pci ors #:R>C Satta s.Fh a funttton FE LCR) wtgne 116 Foustes tranapgin aa The pe fi BROCE given by BE pee NS gy et, conn sal at port 0 6 Ploy: "90 ae (cdl dx < oe, es" = b * L a InN oT Q)* fp £y): fen Oe eaminy 4x fA Some S>o, then Foy (2% +aiy) eG > dx a b + Me Ref et (a ey ey? Fi A e 2 aX +iys)® Fy): e T (ys) ft pale +iys) S| +o. 7 We now pein a G@mplex Change 9 VoSiable Z= =Ltlys Crake Possible ty guchy's theBem) and gee that the abeve fk Guat to em tus? item dzes.emys)* Notice that ie S=d reget that fCx) = on Sodinpics fe =f bla. Aa £ 6) 6 State and piove stngulad Value eecompostifon, WP Singuich Value: Let "AGE a man matate Then Square not § Ha 9, ATA be cuted xingule Value 4A and. 16 donotect by & ‘oan te etry » Sa=frg ___:80'on, Rank § A“ Rumbeg nongas Mrguica values g & géfven the : q ContRuctRon 9) Gngulss Value fecom portion Step 4> ombides the given MARL A, znd the. Agendithon&mal set 9 Etgen vet Ba, the Etgen yectts in decnecsing Ades depending See, v= Evijvevs_. J SiH Moots @ tho Eigen-vabies Called a& Singular Be fy @ Slagonal mathit ‘py! using nonzero Singular ‘Values, ond A, {2 the 2ame Gige G1 A’ with 30g d-fen-s=ja-l=) The tabulated value J t-diatatbution at 51. 9 Level g ge dpen Ps ty 22.201 be, topes 2.k04 since teat 7 ta, = 2.97 t= 2952.9 Ho te Reported at 57. Lev 9 SFgntyEeance Mote: Ip toa < ty, then ve atcept Ho Lb tot Zt, then ve nepect Ho Bh AR 1 Hhdown acy Himes and the Number appcadtng on the (die) fortlonss the piiowing frequency déstetout? on st) a)! | [a Js [« Detect sl as fof setic Show that the die fy biased at 57. Lovil Of sigagitance (Given bet Hy. The die 12 untfased Hy the dee 18 asedThe phequencios tn the given data one the obbeved jee joe aumed that the die fe unbfasedCf-e-, hen, thrown expected prequenctes pt the Num bess 1,2,3,4/5,6 OP 2bY - yy eath ont a 32 sy. uy | 44 unda Ho, X= [ - Ee JO = Cues (33-04)"4 Cs-uu) 4 (sel), Cou-ua)S (bora te uy ay uy uy Fae VE CPS ah +06 4 10> 4 10> ua ue uy uw Tae Yor B 2423 + SOFSUTEO ie Se ee é wee [6 4 1UY) 356 4 36+ 1m + 256 = WorlUNtoese4ac rotary wou ue yy Wy ue Tm va go8 = 18.3636 = 18.37 rom he YE diataibutt on table at SJ Los andl dp=n-4= 6-4 es XK = 10% —— > A¥om the given data 2 Sirce Katte Kak te, 18.3636 >I.040 RS te nejetred at Ss. hos nd the Singuly, Value decomposition y Ae r uory fai 2 ee sib ale [: q ; Lig -2 Totb4 UUFSb S616 Guts 6 BIFEG Igy Se-le tSy-14 1964Go-A 100 Yo 160 «1F0-A IYO 4o 140 2e-% el i... Iwr~ S600] +40 [iyoee | a) HuUo)-Ior[-iortiuyer)+gofucr +420) = 0 1WYOA+ 10000» - 14 Vooeo Hitoo +22 cage [3702902 4(- Pabeyr=IU Yoo) +159 OA + Jeno) +I S200 14 Yoco c+ eseRdae FUSON-a2uWAtO>O => 3- uSos24+32U00 Azao BEN A-dI)KI-0 = [8e-> I Yo " 4 %, ico Vo-> 140 %> qed” 20 4 ho uo 2o-rnt L *. F Pd Az>ato fa Equation @) Bo-to too YO x a "ato ee a 2 too 1Fo-3b0 fyo [= fo = lip. ee a yea f: & 140 2e0-%ot Las} Le- wo tue ate) FY OLE =9901 tievtetuot,s= 0. > © o +6 aioe é) ory tiuotp-ltoxg-0 = © key UA eet toy 41 Cong iue)—CI90%40) wom © ana fe BP | 22 = (280K 1Ud— Gey) (oor) —19 022 *tHel, mae 190 12 = Comt-19) = Cox) 00) pedo = <2a 2% ep =-m | aa Traut ft pay tyooo¢4oev -Ba2e-4eoo © $32.00-lov00 2léeov -u 324 0 URPE wy a1i0) 4 opm che fo ag Yay SS elf 2 a e & s put »=40 tn Equatfon @ eo UO | fe “10 100 4 0 a 2 | 6 19 FyorAo 10 w|qo | > | ww go iu || am JF » x3 HO ud om -A J LJ ES wo tdo Lo OX, Fit,+UWoL, =O —> 2) Lt Gor + Wot>=0 7 (4)) Rox, +!ot, + oXg= 0 —> ® G2 O [- oar Sg, | ae ey 22D _, ne. 00 ~S00-. ipgper oe? —— Typo- 4000 ~Boo-Lo000 | pgOO -SuED -1 0800 Bee = R= 43 othe ; oe vo np - put »=0 tn Equatton (C) yo-o wo ke 4 eile go to Uo %) too [0-0 1ue mle] o too Ito [Mo wm |= a wo tue ro-ol Lxs e. ue two 200- EX Gor, ttwtz +40, = 0 —> [ook] + [FOAL TIUOX,= 0 —S> © Wot! +1uet2 Pox, =0 (a) “3 Yor Lis lento Poko go (0 Wo From and Yo= Bop! YO-loDk UO © fe a 23> 8k190-100¥1 OD +%4 = rR KB = Mo seme tyooo 6800 2H-4oeD ~—13609- L000 #200 S44 2-8 =X OR rales oo aa 7.” [ate-=o jo check ee po extras C093 [8 94272 Xi kg2 [a 4 aieS 2 4-8-2 = Oo t L¥g>= Ry Xs> GB ae) [2] 3 eA Wye ta, tye Xs Tan! Tag igi me TPB = Gaaw = A tai Sal: Biss ices--Ve[By Ve a 3 Yo J = Tx) = Sato = Waeie= 6STo y= VA, = Vao= avie=3 Sio 2-1R,= VO =0 Now we waite Bingulad nonzero value in pointipal diagonal « eS a A=[e, vl: a Ade @ Biemmame 229% EN ° = b= pean © 24 o 3m e_ aie \ sg peasy, om 19% See [ | M3} °° [ |» ‘ss : he => 1% - a vp Now Abas py > i 0 “1 ie nn a & 3-2 ee oe a\* Alwasfu wy hs [eres : 3] i: Lg} *8 = | ese ay | Loy Ee SES ope un yf gee) rs . - @3 2-0 2 AS) ee a) Ty ae | [ we) a ere! Lea, Vio ee 35% [7 ae aes ie a ey ot 2] Wie\ . + +1 [9M Yao) Bes, = le w Ow. Uy,pUa>> [323 )) = [2 2) e 4 and Ug are Brthogonal Vect sd us(ua,us) = [Wo - Me Mio Ho The cingulad value decom poattion Q A FA AcuAv = i Yq] [ ite 0° - Ya Pa 73 Ne wen: ioe [+ Yer Us ts Hs fad yyX WGOrOK2 HVE — EMied2 HOVE HOKE Ae [8m “Ase A OF! aavior 2 + on oa 4 afer) poy-2_ reser hae 2 = 3 3 sg OS tet Yio *Ao ne a a “ Pe -| a aviio ute 4S Yio sf) \bfo/, 28 8% Von % ee =a [Ee [ Bye eee axe LyaGots pS 1 xuliet 3 eo 1 Eo Ge Vio Ge Ta t2-) 12728 uM TY art ura) See fs F -a -! 0 10. Find the Efgen wile and €fgen vectd§ D nfs bs. e | oO Tre Elgpn value wre srepsescrted by using D tence Cig veck % Mepnesented as Ve ‘| ule | c. then the etgenvecté f Galcutated by using athe Guation, [A-MT)= 0 aes: 5 on a-» -1 0 cone oy os +) ~2-A DB eho ea i oo & oo} ° o 4-n =v (C2-HCE] - [scr -0] +e [3@)-e Ca >») 2k) [at 2a - + 7] +1 [3-3>-9 to [e tot o} = (2A rtp a)t 3-3a 40 = e+ 2d-t - DS a7 S-Barrt+r oJ = > 8=> RMekcodew-.*(r-DENA-D= 0 pit |, jal E A=d4 = e21 en Eigen valle ge U=-), tard + %20 find bow cgenvettcs for az -! AM K => AACE o> Gaon verth [a-xtJ “1D “ o =p 0 [= 2 1B =@) prd-> 3 O wel in an ® ei) -) o Ya f) -} 2 at) Oo wm ||? Wee a) a3 o 27 3t1-%, +9%,2 0 >@ rom ag bt — aytar,4+0370 >© i ch 2 ) ovsxota +1%320 ~© mee osta oo 18 sae ge i a a ae > f-o 643 wre Now Find ; o ia verth tor =) ML equat ton) pacha) [43d ° = 2 o 3 @ fon atl aw te 3 it 3u)-242 t0t- O> (bi) [i aH ile ov tot, 104370 (2 wo saa s 7G sf tiswta tS => — = 0-0 0-0 3 ao 2! the ci vain, cae Yat andy?! and Etgen veerhs ade Pe) ana fe)@ Getond dopee paabila ty whe method g least Bie) 2) (ie Fammet beier ies The @quation fe yeatbz+cr® and the n&imol equations axe Y= ans b&w WO Fry Eat b&w? +c B'x3 -O dy aes eter car! oO) the value, one taltelated using the follontng fable heed ne ay xy Le. 4 Joyo tego 46 2uyo 4ysso at 34 upto | msto ash | 6500 | 26000 s | sas 47895 oy 1as~ abner Dey =23%5| «ranges gubitttuting thee Value, % the ndmat equatfors. 0 6,0 scenes GE? Bartle bt55C =494) —@ 45Q4 SHD FASC = 8377S -6© 55 a4 987 b 49946 = 35S -O© Save the equattord (D and (© and diningte VA ase a" multi py equatten @ by 8: —e Sf 95% = ee LOL EES OTST = IDIVS [sq 4 TSbIDSC = 2379F Cree eer eS eiDerietr “Zeke > ob+boc= wso —) ete ne equations (®) and G ond ebininate, vartable ‘a’, muy uation ne "legal Ory: 5 Bept log b+ 6056 = 79,65) — 50+ 16 wees ce aac Rf by 4 995b+979G = 99355 Oe oO 9 © Geax 5 bt arAC= 49355 D pep — B7e6 2-12, WY ae et-39U6 = 12F04 —-@ g equations (H) and @) and elfminate Vasfuble 'b lebt60G -aosa —>x¥ by & era 12819 60b+394C= en 4394 C= 1250! YC= 1904 © oS Ze UG is y ~lud =e 99 => 2 2 Now neplace G Value th éqeatton(Z) E232] >/@238 fob+60G= 26582 > lob+bo Qoe)=2059 => 10b+8GR0=2052 = b= 252-1680 lobz 37a =>[bz 39.9 Now veplate “6° and ‘co’ Value en equation (¢)) Satisb+55 C= ay] Gay 18(39.2)F S508) > F2Y/ > SarsseziSlo> FIYy) 5a$9098= FAY. => Sa= tay1-209g sa>5l43 => [as 1028.6) Nol Substituting file vats fn the equatfon Y= aperrer no 4 yz 028. 643792 +98 e I. find the Ove 9 best fir g the type Y=ae*h wo the folloctng by"*method, 5 leit Syucres « Y= ipso, * Taking beg on both ides bt Logy -Lo4 w+ bog e 2 bogy = = bela yo at B® The nAmal eqpations ore ayeaateF* —-O guys AULT BET >)« HY fp ae 1 WL= 0} : 5 iz ISkuB= 5.9 | @S 1 12 ayes: 356] 49 4 Is Geis =l06R] BA ie 2 x19 Issy duy EN 546 ALY -40.92| Gxr=3 od 2 @quattons (1) and ® : Now eplace Valle, Spy puss 6 FO aun + Bo0B = 40.92 2@ gave the above equations » multiply en © by 34 and an @ by #8 tof +hSeBz 199,94 AWA FISMB= 204. & Bes 5 belo © 0.0asy ~Buy Bs -E.96 am Now veplace +B vame 9 Suction @. 5 Ayaylo. o2sd)= 5.96 SA +0.08636 > 5.6 Bro 5 46—0-08636 & Gi QTaby ney, 94 or 420.9992 = 0:98 or 5° on But Loy A> ae | 04 Bodog, t # &= 2° He a= ti te a= 120592 Yor alee - \ yeasel a