Hill16 - CHAPTEK lb I624 0 3M 10 ”Away of mWr tamrm 490...

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Unformatted text preview: CHAPTEK lb I624 0 3M, 10 ”Away of, mWr tamrm 490 any WM an M7, MOI/[214V M0413, holds 70er era/«150‘» of +11 W. b) [a- 0.- 2AM , I= Clank, 0 I‘ 71.2.. IO=PM: :9[.5..5] IéZ—Z a) La 1 : n'ncreasecl today and yesterday “fem!” ‘ 2 = incr£a5ad toda. but decree-S y 3 = dacreased today out increased yestCrday ‘/ = deareasod todaAj and. yesterday 4 2 m 1 o4. o I— at. g The» P=P =2 A; o t-otL 3 O 0L3 O l ‘ IL; 4 o GC 0 l 70W 3 Se +L‘e. shat Space as propalv 416/246ng b 39.680 +9Morr0V/5 s+a+e wul ’Codeuf a9» 6 estuda )ia‘d , ~ . (if: «1:; SeCo’I‘d <01)?“an 4‘34»? +0 +odays Fd’Si‘ “MP“‘AT Tim stem wmuaud m in WA Medea! 12: flaw WW" 4W“??? Maw etzdu 9% (9,03,44,24. 0(qu 09:16ch M “‘17 ”f“ 51% ' 16.3 4 6L) P2 = 0.3 0.7 p5 = 0.175 0.825] 0.14 0.86 0.165 0.835 P10 = 0.167 0.833] p20 = 0.167 0.833] 0.167 0.833 0.167 0.833 No“ 163—; (b) ?( rm n Mafrm m) W». W) = N If th frobabwh, 4+ WIN MM 'fWVfi] {/1 0.5 J PM). 68.3. from now) = p" = 0.593 m , Fa‘bjS , F5 =0.o875 ,. ?Io=0.°835/ PM: 0.0835 (C) We ftM 7m: 0.l67 7rz= 0. 855 00“}:jo Wow A grows) ije, @vovj mo cf PM) Afpmadlw I; flu MM Trobabs‘flw . '6-3’ZUU Ltd’ £41105 0 (MA I dwTé, M a 0 M al W0 been mmAeA/ nérech‘velg . P‘ [ugly 'Qir‘fy] MM 3“ 0.91 Lb) Poo): [03“? OWN] 0.071 0.903 m Pnbdfib‘h) Raf 0 dfilf‘ WU record”! mama]? {A 0907 (C) PM): [0.97 0.0!] 00] aq? TLa frobabtfi’cj 130 052‘} l63‘3 A) Transition Matrix, P = 0 0.5 0 O 0.5 0.5 0 0.5 0 0 0 0.5 0 0.5 o 0 0 0.5 0 0,5 0.5 0 0 0.5 0 (5” 0 062 0.312 0.156 0.156 0.312 0.312 0.062 0 312 0.156 0.156 p5 = 0.156 0 312 0.062 0 312 0.156 0.156 0.156 0.312 0 062 0 312 0.312 0.156 0.156 0 312 0.062 0.248 0.161 0.215 0 215 0 161 0 161 0.248 0.161 0 215 0.215 F10 = 0.215 0 161 0.248 0 161 0.215 0.215 0.215 0.161 0.248 0.161 0 161 0 21s 0 215 0 161 0.248 lb‘L [6.3-5 5) (CodT’D) 0.206 0.195 0.202 0.202 0 195 0.195 0.206 0 195 0.202 0 202 p20 = 0 202 0 195 0.206 0 195 0 202 0 202 0.202 0.195 0.206 0 195 0.195 0.202 0 202 0 195 0.206 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 p40 = 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 P80 — 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 (C) wmmm}% ~PIAA01¢ m=7T1= ”3 = 7Q: 773-:(22 l6fi—‘ (a) P Has one recurrent communicating Class; {0,1, 2., a? (“Plus three communicating (Masses: {OS is abSorbzng and,there{ore’ recurrent {5 2.; is return—grit {33 {a transmnf Ié.‘1-2. (a) P has one recurrent Commum‘catt‘nj (glass; {0' 1,1,3; (5) P has one recurrent communl‘CaIz'nj ch55: f0. 1,17; qeh'i Tk'ts main}: 1145 three Communicatfns Classes: {0,I} is recurrent {2.} is transient {3,4} [5 recurrent 64-4 “’5’5 1—1.“. are +0.20 wuss“: That: (:5 a“ (1355 I 59 “)5” iO/UZI‘I} 2A4 $63} can, MEAT. [425 M SM (£1.44 '4’”wa “gped‘ioq. , cried Fro“ J-Lc dcfzdh'm, Fm” Hu. M 7 ' +14 (Muted Fof +Lu. $*‘°-+“ ‘4 $0,025} is 2 M¢ Hut. [5145-04 5.1123} 2} 1.. is ‘1. ch.“ 30/9414}; Haaszed- amt (33 is (ca/trod. y.’ Emspzofies.) ”HM- [MAM “2—3 155-! P: [:9 [(2)01] Fmfif=p =9 MK‘+Cl-/9)7T>=/ 7?, + 7F; -—- 1 => 7a (:17, , 4—7 Ida-5‘24 Must show that 11:3 3 ’31“ 40v- }: 0.1, .. 1. M satisfies Hue Sfeacly state eguatt'ons: Tl; =igfi51‘r3, {arJ':O, 1": M 4"" ‘E’Tfifl. Sm“; Pu“ for «“3, this is easily verc‘§.'ed. yo no ‘J 6‘ 'mce the Chan-in is ”reducible, drift-041.6 and positnlue recurrent this I5 the unukue Soltd‘l'cm. ‘65‘5 ‘5?“ ”1:51 7TI<7TL=7Q : 75‘; T; 3, ’5": 10.2 7‘41 5T 4731b 7&4;th 060157 Me If ML 74164611319 Stars to. 16-574 Rom flu oflwwwmdm can find 7n: 0.344 713 =o.585 713: 0.267 Wok Menu 11w giddy-m ”wkats‘a/m 7067 A M5 N2 0.345 M)! 0.335 Hard-1.1113 . {6.5-5 Ia; A$$ume dcmand occurs «Rev fine duh/cry: ‘ ‘5 K § *- 1 5” W7 1 .-l .3 A .1. P a .1 4 l .6 o o o o 2 .3 o o o a 3 .I .1 o o o ‘0‘ 0 .1 ,3 .4 o a 5 o o .u z .3 .‘l o ‘ o o o .\ .2. .3 .4 '3 o o o o .1 .2 -" lb'Lf “9.5-5 (comm) (b) 1!? :1: :5 (.133, .n‘bq' .I39,.:1€,.Nt,.no,.314) (C) m 5% mama-ti man PM” 5M 1;, 25 £2 MM = ”may. pfa‘m‘e 1‘4 +27] = WHO-'74: 0.0696 (0‘) P-{enwrjmwy dzh‘min = f; Hmzz M177“; i=1 0.l3?X(0.2+o.l) + (“37on =09556 has-6 For 0L (5)8)p0licy with 5:1 and 5:3, cog-.. 0‘) = 10 1» (17’0“.-.) 1- 6amax{0;3,a} For *9. <7— {5:0 ”“501" {4’03 for [(432 thus MO) = dummy: 35+ sofgq-‘n flow” 2 35.2. KL!) : chUJDtfl: so + “CFO-3) Pf‘ofij”: 51.1 Kn): E[c(2,De)] = 0 *‘50[€9‘-1)P{D‘¢j}]? 5.7. 3“ BABY-E36530] :0 +60 (2-3)]? -' ~12. {1:17 {Dt‘JH‘ ' Again {or a. (1'3) Poh'cy. Kt": "“H‘u'Dt-rna} {9" Xe‘f‘ mav{1‘~ tH'O} for )(t 22. $0 .080 .lB‘f .368 .368 P: .080 .:8+ .359 .359 . 2-6" - 388 . 36$ 0 . 08° . I84 .368 .368 Solving the fife“, {bit 81M¢L{;ons gives fl=,l¢$,m=.152’1fi=.353. chcc, that long-run average, cost Per week :5 «3:13; ;K(j)fl‘. : 30.37 JIO ) 195-7 xh‘gzrmaxixgz—ptfl‘o} {war Mil m°~*¥X¢*Dm,0} 1m max «25" .368 .358 O , 080 . :84 . 358 .368 So 9.; . 25'! J“ 3353 O , 680 . I84 .36: .36; Solvhj the. steuly state. e$uaiims gives ”of-“.1913”? M735: ”'1 =36,” #3:.‘65 5’ 11M EH2]: C(xd): 0170+ zfi.+81Tz+IgTTs=G-‘fg A-bao é“ ”if, K':P{‘Dn+|=°} + P{Dn+n=2'} + P{Dn+\:4§= 3/5’ 51=P{DM,='} + flown} = 2/5— P = PLDnHH} J’ P1200953} : 1/5 2| Pn' = P{Dm‘= O} + P{D““ : 1?". PI’DnM: 4}: 3/5' 475' 3/; (6 (5)) Since. P 75 doubly Sto¢hasitc I fit“; -:. V1 . (4‘ KW E[c(:,1>.. )1 = (2/6) [3+ 2m] + (1/7)[3+2L1)J+('/r)(l) + +(4/r)fi+z+31-: ?.8 km=£[cc1,b,,)]= (1min 1m] + (ya-Man Lz)j+ yes—[2+1] +(Y/s')E ”3-1 = “-4 So long-rum avermcje cos“: per km“: Hm: (5 9,? (V1) + 54(71):: ?.lo. (a) “03 WW"? ”“ ’2’“ V‘" W“ n} = oz M 0.64 0.16 0.04 0 16 5 0-62 p2 = 0.64 0.36 0 0 P = 0-594 0 0 0.2 0 8 0-64 0.64 0.16 0.04 0 16 0-52 0.614 0.191 0.039 0.156 0.615 0.192 0.039 0.154 P20 _ g :1: P10 = 0.616 0.193 0.038 0.153 ’ ' 0.615 0 615 0.192 0.039 0.154 30; 0:2, f=o.o4.~ 4:5. P=MS7 h=lo , P=O.°37; n-Jo, f: 0,033 0:) m: 0.615 , 7[._= o_nf2 , m: 4038 , m= 0,154 (C) lava-rm awn-459, 600T rev peri‘oa! = $50,000 It; 41/110 16-? 0.195 0.174 0.232 0.195 0.192 0.192 0.192 0.192 0.037 0.046 0.026 0.037 0.038 0.038 0.038 0.038 0.148 0.186 0.102 0.148 0.154 0.154 0.154 0.154 “Jr! a) T . . he process $4tt$fl¢$ the four points listed in 5¢6.|5.3 anon; m I Let 0 : WOVK§ng l 1 Failed Markovién. a \ L) Moo: ‘i‘J I400 .pflgg'J l.lS P -=. o .9 .l M0,: I+.9Mou -I>Ho.=|0 ' ~55 .35 um: t+.3sH\o-QH.9=LS‘1 M”: | 4- . 65 “914: fins-1.5 l. - . ééz (a) Lot 0: dyadic—Mao , 1:: dawn, 2;.- refm‘raol 711m 0 1 _ 2- all a P— I[o? o ; j 2 .93 0.1 o (L) Frm sec/4:5, we. We, ILL/=14- {:3 Pl‘kf’? 90,]490: H' o./ Fla MM F‘O’ J71. {Plo=l+ Flo j Fh=/+ alfho {PM = H 0.7 Val F"=I+H" Wan-I'M {F"=” ’1‘! :7 l 4— 0.? (Joy [1" = [0 Vol: l+o.9Poz+0.llez [4:2 :1] Viz: [+0 M Aid fly]; _.._.I F2: :. H 0.? Fox. 4' “(4'2- Fzz = 2.07 Tu arid my, a; 47’ rm mm loll/m" afzuafie'mj 45 /o (C) I4 tom/d 1mm W2 duet; #1 Wm» 79%? l6‘6’3 U") (0,!) (1,.) (A) (In) 0.7 0.1 o 10" (0.!) a? o 0,, (M) 0-7 0.! o . .. , _. 09 1)) p.33 3 #3 . Sa $olvuxf #P’W' 9AA TT-l-l but {11* 77}??? Tlu/s 1433:2151th («#4643 1‘“ ‘KPs‘hd .003 r-Lwrrcnu +£~¢ oe 5+3“! (0°). 16-3 100-4 M Transition Matrix, P = [0.25 0.5 0.25 ] 000 .375 0.125 .438 0.188 .375 0.125 P5 = [ 0.15 (C) ”00 = l+ 0.5 “50+ 0.25’420 “09 = b/q F“? : l+ 0.25'4‘0 3 {1‘1"}: 4/3 (41.0 = a+ 0.5(lw+ “35,00 Hot = H- 0.25HN+O.35H1| 000 0.5 5) p2_ = 0.375 0.5 .449 0.4 0.15 0.45 0.4 0.15 .451 0.399 0.149 p10 = 0.45 0.4 0.15 .449 0.4 0.45 0 4 __ Ho! = z PM = |+ 0.76th 9 if“: =23: H" : |+ 0,151.40: 4' O-erlz; F34 = .2 [‘92 = H- 035r‘oz-r05fhz H02 .2 % { HI: :: |+ 0.75IJ01+0.25I4'1 =9 P12 :3 P32: H— 0.15-[4.2+ 0.5,»,2 Pa: 2 '6'“ 0 3‘3? 8'??? 8°33? S°1uti°m ' ' ' = O . . . (a) Transnzion Matrix, P 0 O 0.5 0.5 1 0 0 0 1-51 = 0.154 . 152 = 0.538 b) . - 15‘ )4" 6 o.I5 ) I 25.0} 1: = 0.154 ( 7r C .. [0.538% 3(0. 4 ( 4 = 46 7 “Z = 0.154 (c) P“ = H- ag]; [4w apps/4,. + 0,0525/139 PM = I 4- 475/4» 4- ARE/be + 0.125/4:0 [Jun 1+ 0.5f414 +05wa Pso= 0+! :9 #00 = 5,5- , wkv‘éé 30.42.4746,” redone/I f/I‘ae fat/$125120, 16-9 16.1-! a) For 444 +0.43%“ “247i": P00: P77“ 9 aux—1:3. I P‘JH ‘7’ 89’3” d“ 'M) P: I O 0 0 ‘5 ° F ° '3 “ 1, o P ° 0 3 0P 0 0 0! (“Class I: {O} which is cheer-hing Class 2: {1‘} which is absomgmj ‘ Class 3:{l,2, . . .'Tq} whigh (,translent (C) Ltt fix: P{absOrbft'on Cd" K aha“ stow-1' ai' l; FOG—a 6o3=0 830“ £33“ sud. misc 6" I'L-.'\\*1- ,a/6 9mm? flaw-=9 3L 8% we ”at“ 6.. =Q+P€zo —x> €.°=9*P%to-°€I°‘ we” 6:3: t—é» ‘4’ 6?"le garage“? —D‘€Zo=.6& €23“‘€Z° 016"“33 d) From Haw, same Formulas :25 «1A Qar‘f' o) wt. pb+aiAz g|0503$ 6‘3: 0 62 620: ' ‘ It, 623: .&86 If appears 'Hmf .97‘/,_=?drf{f +0 1" .pz V; 2‘} drl‘fi.‘ to 0 (a) 0': Hub to Honor warranty 167‘2- I : Reordu in lsl’ year ,1 : Reorder in 2nd year 3 = 330“" '2‘) years or owe! a a L 3 O l 0 O 0 P' l .0! 0 .97 0 ' 2 .06 0 0 .75 3 o o o l (b) Orobabilzh, manufacfuf¢r has to honor warrant-9 :s-w (‘0: .0! {3° 1» o fio +- 39 g, 1- 05-” ‘19: .0551» +- of» 'I' 0 f1“? 1'.9{‘3, bu" €003! and £50.20 =7 4-” = .0] +n‘?9f,_° $3,; = '05 => 1‘", z .qur = {.7r% lb"\0 (b) Balm We _, 511', = 271] 47‘: = 57R) +2”; 575—.- 2m+27§ 271—5: 7:1 7Q+7Tz+7r3+ ”0:! (6,) 30M “Wm M 3‘1" 75-1 7%. Fl: ‘63 'Z.(a) g+¢¢gx Wk.” oj jobs 03‘ H9. W4C Goa—04’ 2 Z 2 A A @ (D @ ® 4 4 4- %) QM—s'kh créi‘téms; 2m=47fi 67f. : 2770+ 4N2 £75,: 27C|+ 4T9 2m: 47?; , F0+m+m+n§=l (a) w. cam aura) 3e? “=(783’éifg’7é) [5’11 ...
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