Mathematics%202%20-%20Theory%20Part%202

Mathematics%202%20-%20Theory%20Part%202 - 5-6. INDEFINITE...

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Unformatted text preview: 5-6. INDEFINITE INTEGRATION M2—T-29 5-6. INDEFINITE INTEGRATION W 11% kt?! =3(z)+c Vane-(4le puke/2.2. c is ML PM: LAX 41.01.) = tog—3(a), a: 60131:). 3.5 gamma 6301,19), xféxz than. 41. i4 W 67L [11,112.] M dififimm 37’" (9519(1)- AM-o by MW Vaflm Thu/am, I ham—4mg) = 4x30.) (air-x2) m c. 5 (29,242) Tm c 6 (dub). #ch = 5'ch —3’(c) = 0 41.09) : 410(2), v‘ 221,17. e ((115) 6(7‘1)“3(7‘f) = bfiiz)—g(zz), Waspzze (4gb) {5—3 £4 a. W Maxim cm (5.11,) [100-309 = c, m CGR. L4 am. H96) = 300 + c. v z 6: (calls), (HTMWZ: er MMMWQW ICR, m —..~.._....—_..__——-— HHXJ-i— (xfldac = “(2942:. + I (2942;. Pat: it; M2011. + 13994114] -.= ifflxjdx +§2J3malx [M a} Mafilrcd) = but) +390 (by Mam 0!: Mm) thm+3m14x =It(x)d~1 +chx)d=c . 34¢ 3W, it “‘52... 5,1 cum. 'mtagnalnfla mam W, m“ Hindi) Hut") +---i- “(1)141; = [wach +ijJJx+H+§WyL 5-6. INDEFINITE INTEGRATION M2—T—50 (3) Tm 5: file. [ac aLx= 49. (20:12:. (Mum. 4e. aw.) P : of. a; hjbpcybc = kfijuxmx. _—_ 4;,ka) (Rule. 01 “25mm .—. kfk(x)da_ (a? Wan 01, paws-dive) (4-)de41 3:“!!91-442 B W cm. [d,fl] ch difimfiaML m (age). a'ct) is W gm, (dig! and. a‘ttlaeo, Vt €(d,flJ. '- WC”) =H"). Hm ‘5, £6 a dibfiveM/MLM 61, x mmJb) am an Ls a. AA'WMW 01,1: cm. (aged. Henna, «am a. aflmm Win10}; em (0H3). . it? kfgnfl = 44' [gang'm = b[g(t)]g’(t) 4%ng = Ib[3(t)13'Lt)aLt .. has) = [Hgmjg'mdx “(mix = Ibf3Lt)]3’(t)dt A5 311:) Ls W MAL mm—zmo, x33“) i4 anti-m and Wm lug t = 3"(29, m. W'm em MwahMMWMMMMaW'mot—m. 5-6. INDEFINITE INTEGRATION MZ-T-Zl (5) Thwm 5': y, Itijdx. = Hz), mm Ib(arx.+b)d.x =é F(ax_+b) M (VI—.3 i6 W on. 561141 mm 12. (4450) Pg: Lu: az—I—b =1: x=—i;(t-bJ =gtt) 3-5 f n ma)?“ ‘ (6) Thuam 6: Hum] Hz)“. = +C’Mh1 ’n-i-i Wflxl70mbf'mmfim w Hz) 4:0. Plan-0t: La! t=b(z). Sag—i =f'(x) Sim H025) #0 mad. W, f=H1Ji6 n 1 m-m. I[k(x)1nk'(x)dx =jt“ out = t + + c n+1 = “MN” n+1 mrmmrgugmmwfimmm t' is W M mam, Hx)=i=0, :1:¢'=Ec€t,l::]J mm 01'1- =b3lkIKJI+L +c #6") Punk: b'uWMW-W.Hmbi6 -. PM) __ 5'69 4 _ d1: _ JflAx—Jfl.x¢u‘_]? -la-gltl+c +c INDEFINITE INTEGRATION MZ-T—3Z 5-6. (8) 5Mx 01.x. = 1173 [maxwwat’xl = agglthil+c = ruminant (max—mar.) Ax N010, jmcxdx Wax—def: _J -mQLxLofx+ws£¢7'x 4x max—M1 z $(Mx-Cfix) in Wax—Mac -_-.. WIMm—wtxl +¢ M60, Mac-c.0171 = I’M”; 1:. mg: 543nm .-, Imacxaix : = +c' U?) [second—x. z ElfmUT/q-l-z/ZH +c. =h315£¢2¢+W1|+o Pmt: F04, my: 1:; ha M'm, 2L=1=L2k+l)nz,kez. coax :/=a Md. I+S4Jnx $0. I+Mx coax. Naru], 3424x511. =1 =Aux+mm =F0 5252:.(secx-1- buzz} in: sax-r- Mar. _ 553421+ML1mx 41 Senxd-t‘amx =fétsaax+tnme Ax mx+tamz = Eng-zlsmxi-tmxl + c '2 A160, Mac. +121Mz -_-_ "Pi-“ME 1mg": Pram"? hm“??? 5-6. INDEFINITE INTEGRATION M2—T-33 = (I+=Ihvm"“/z.)Z _ Hm? (I—mn‘fi'znwtanxxz) * l—taflati = W ("/9 +392.) [$342,494 = 1.03 [mm—rth] +c =b’glm(%+%)|+c (IO) Eula. gk fl PM: (ii) 5’, 3' am. W m 1:, mm fur.) 3Y1) Ax. = “292(1) -- Id-l(x)&(7t)dx, a; 6:11. Pmt: womb“? JG: MM 6} fi'fiWAfi-‘dn, cl 5&[HKJ3MJJ = “293’ch + 3(K)b'(x) '- 5:? MMW 03 'em, Manama) = It “@3720 +3tst'txM dz = “5003129 dx + 13(295'0042; Ib(1)fi'fi=¢)4=¢ = h(1)3(z) —- “(’(x) “9942c (i) This i6 MMQ 5-6. INDEFINITE INTEGRATION MZ-T-34 I = 21W “Izfi.22¢.xa{x :‘z. Zz+aL—- 1249‘“ aha“- : 1 12+“; __ {(2114-42) .a2. ‘11 W = 1 1w fimaz “WE—+5— =1 2:14-47- — I +dzfl13le+m'+2‘ 2]; : 1W +azipzlx+m|+zc I = 33W +§Mlx+fi§1l+c 1—4?- ~¥flqlm+¢x£a1l+fi ’2..._[ a 4—...“ 2.. (12-) Nata—2.1 Ax. = ‘1:- Mai—x1 Pmb: 1: = jr’m 4x =f1./a1::z dab it. nyo a+c( ) —_.-' at. al—xz- —§ 1 (—-27¢.).1er 2. a9.__x1- 2-; '2- _a_2' asst." 15 out. = 7‘ “‘4’” ‘ W‘“”" M W W1 =7L 4-19— ._I + aim 3-. +7.; .— 2 2, '2. *IE ZI—ZJQ’QC +am “+2.: 1 0.7- .41 5-6. INDEFINITE INTEGRATION MZ—T—ES Us) Ia“ [mg + 3'00] Ax = e‘wc) + c- Pmt: {@1500 dx -.-. use) 58%;; _ jgwfie’uxyx -.= ext-(2c) —— 5e," magi: +c. fexflgtx) +5'cx)_]a£x. = 2,1509 +c. 7C. (14-) [QQ’Lbed-A -..: ea (ambx-b¢mbx) Clad-b9- mr. - a, = e. was: 9)+c W W m9: ‘1 , me=__§.__..-,ab:1=0. Fwy I = e. what—Ax. =. mbxjeAZ‘AL—HgimbxjeaxdaLJAz 47L ant. =smbx E... —bgmbz-de :1 CL = ambit 2:1: _. Egeaxmsbxalx 01. a 412'. :11. a: I : ambit. ‘3-__. _ 5— [msze' ., -J—bmbx E—Ax] a. a :1 89‘. b “1. ha ax : 5min: 9;... _. _._ uflb'x. e. ... __ jg mbxafi.m a. a1 a2. (11 z, 2_ 2. e ' _ b 61+!» = E; (ambxubwsbz) ELa]: +(__—-—a2_ )c, '2. 7. az+bz 3:11 . _bmb (a. +b Jb a; I ~.—. .5;— Lasmbz %)+ “L ef‘”L . I .—_ [ambz—bmbx) (I) a"'+b?- New, M (L :: ILLOSB’ banG ta: {ah-bl 0. Sim bx— IDLme = hmflmbx— htééuewibx -.—. 12.54514; (bx—9) = W slum—9) 5-6. INDEFINITE INTEGRATION MZ-T-—36 admiaafihg w.(o, cal I : (1241,2— [JQZHJZ Sim (5149)] +C~ 2“" : .._...———— 5444(bx—B) + c \/a2~+b?- le9: Q ,sxinflz b ab$o a1+b1 d1+bL ax. gaz- e (55151413!— = 1 b1 (ac-.0152; + bimbx) +c a +- ecu. = wS(bx-9) + c, Va7~+bz 7 - 9. DEFINITE INTEGRALS DIFFERENTIAL EQUATIONS 7—9. DEFINITE INTEGRALS DIFFERENTIAL EQUATIONS (1) Ma'& 93 ' Mfg/Lain: I: fing‘mb-BWMCQJMWFBQ | Wm on [dub] 54454. M : F'lx) = #0:), V 2 6 [dub], #:m b £1chde :- F(b) — Fm (2) M 91 MM in. £41: Mggmfim; cp: m, {31 _. ca, 53 £4 am. mm (an aupr Imam— ; -_-_ 4;“) m 99*“), t- a [dig] 011.1 mm M ¢'(t) W W 4433“, .94; a zanu), b: 43w), than, I: L I-(xJaLx =-_ III; f¢>(t)_]¢’(t)att t3)Mm1:§fithmem_ctbnmC-aflj a a [anemia = afo Magda: (46R+) Pmfi : 1 Hz) 4x = Inbouclx +J'QH2LJAx E's—445M611 _.a 0 Nam w: I = [abtx)dx. _-aI Lat 1:..t .'. 9191:...41; Am z=—a=>t=a M1=O=¢ut=0 1:-—:t m dz/&=-1m W cm. Egalaut 44.43% oz, clan/4t as W. a a I = I: Ic-tM—aw = --L 5604f =50 Wit 7 - 9. DEFINITE INTEGRALS DIFFERENTIAL EQUATIONS PM: jabfx) Ax. = [06095125 +1.0 4x [._._a<o (“all _g. _ NM, M I = jobchAx rd. Luz-.z—t dx=_au- A140 x=—a =bt=a amt x=o =1» t=o I = f: (5(—t)(—au') = _LOM—tfilt = fijMt s—ffbfljdt (2' his m mu Wotan) = —— g: “again; I“ [[(xjoflx. = _ [:chde +foaHKJ-ix = o. #0. I53 j:b(x}alx .-. Sfbfiawx)alx th: La; 1 = gummdx Lax a‘x:t d1. Ice—cit Am, var—=0 =§t=a cume x=a=>t=0 O 0 a I = [a HUI—At) = —— 546(th = [a mm = 33500“ [015(x)al4c = Laud—x) Am (6) Thu/1m 43 y}: t Ls W cm [tub], b = b— 4 “w: Jaw =01 ___b__4___——— PE: Let I _-__- Sa- bL¢+b—x) dot. Lu: a.+b—ar_ =t -—al=vc_ =au' 7 - 9. DEFINITE INTEGRALS DIFFERENTIAL EQUATIONS Am, xza. =>t=b amL x=b =>t=a, . 6L .. I = I!) kLt‘)(-d.t) 4 b -— [5 “wt =11 HtJoU,‘ = I: “29:12:. . I: “2901:: = I: b(a+b—1)Ax (7) Thwm 5:91 hi4 W cm [0,110.], [0245(1) DIX. = Emmy“: + {15(24—2941 0. . 2. 2. ML Iaauxydx = so kpcjalx + Lab»(a(_)al-x, I L-: 040.424) Lair 2.: Za-t I'M. W 144.143.5121 an R.H.s, -cI.'z,= --d.t. Aldo, 1=a=>t=a ELM-4L 21:24:12.0 2 a faakbgalx = L b(24—1:)(—-cbt) -.- -5: “2:1-th = jaak(za—'I:)d.t = jaaf(za—x)&x '. IOMbCX) dz = Joab—(x)a(x +Iaaf5(za—xjdx (lo/Lam : (f) 35 baa—x) =HXJ, fozauxfixa-zfsmdx iii) it: Ir (24—1)=-—b(zJ, fammx =0 (3) ufimfl fight: Aw'mmn harm MW mm x, W-mfixfibfia y and. LIZ dw'I/Ltiva 311,32... 3n BamadibfiMALuzud-w “318:2!th In? F(x)g’3hgz~--3’n)=0- Stadibbmwwatmkwmmmmmqa Win—Ii, the. chat“. gmMghM/L' 044M mama 6-ch MMWMBWWUWJfiM alin Mammwumm Wefimflfiw 7 - 9. DEFINITE INTEGRALS DIFFERENTIAL EQUATIONS MZ—T—4O Gimadifl-MM W,Lkwecmbfild.afiumaam g:}{x)wck1nat x,gamd.it¢dm.iva.t£ua {Mid/g WMdin WMWWMMOqu (9) mam NEW Egan“ 3.6,“:193) BaWafithMxM; cud. ILL-mm maiden“ xfl¢(H/x)kmmwhm 71.661. M¢kawm%mmmt=g/x, 7 - 9. DEFINITE INTEGRALS DIFFERENTIAL EQUATIONS 0-:3/1,w& 3d: mammal, 01, m dibvfiuwfid— (11) Lim ELEM Egan and. its Mm: W dine/swan W01;me pkg-Mail? Mafia; :2 sziidd- a. W :1in Wm. Let g+Py=a [12¢ng flmm Gamma: Wat's-H. 33%“: 04.4%, M Eamm'mafi x. mmmam‘d tmwm P16 0. WM, Ifilx. pl both u’wfimwaflmbgc _a Pet. Pat. __ A Fat Nm,e%+Pey~g—;IQ g) 3; (Jig) -:- 9.6%: m 615"” abumctx'm 03 2:. Pat 1O - 11. PROBABILITY 10—11. PROBABILITY Dgfl'rm'fikmd : mumampuqmm.aqumn, Wally, BMeAhymfidflE/Lz, 5) Eve/mt: A ALL/54414,,mmpflidpam U Matilda/mm. 91: [A W113 magi by Capital m All-3,6,1), a}; Maudpaat What: A,, ilk/13... 4-) CMMW: WMMqaaAtgp'cMWMatmfltafmm BMWWWMW.WM¢F¢¢UB calluLaL calm W. 5) W= LMAbamamt. Saogaupdmmm B‘h—U makthiwA hmwmm— mam, WayA.atmmuAbgA'nfi.m m mm mafia», A'=$Lz.|x,e:u,m¢fi}. mecpmmm WUMLLMPW 1O - 11. PROBABILITY a) Monolizwoevw: LfiAMBMM.S¢%MWMm ammAmmaammmaymm AWBWIAMMBJAUB.MMW¢ MMm, AUB={xEU|xeA ensues} Vjaamtemmmgttmam: LexAmsmW. SMmAWfla-Bauw MmmAamLMBiAmmmmMm athAMBmudmthgAnB.h MWc Wuhan, AnB=ierlxeAMxeBL 8) Mum—aux Wm M: LLtAmchemLtd.%AnB=cp,1hmAm B mwmmugmme W. ‘1)Ethfivew: LdAmdsuW,agAus=U,mAm3 MWMW, W. 10) MWWLWWNW: LarAa/rLoLBhaeuf/ntd. £5Ana=¢mnus=m MAME,meng Wuem Wm M. 0131115014417, B=A’=U-A. 11) mflmgfitwoum: LQtAaM-d—BMW.TMM£01WM MMA MMtMBBWfltfl-diyfiamof MMAManmmwA—s. Similaufl, we. mmmms_A.anmmm mM’m,A-—B={er|zeAM1¢B} B—A=ix&UIZEBQMd.x¢A}. 1O - 11. PROBABILITY MZ——T-—44 12)me£témgkaflgf££m: I MM Wire Md. “LAM-ye um, A,,A,_,...A,n (fl32)kam awh'mqammW U. 15) EM: W: Lax u he. a. M AWL 43m amt M U=fx¢.xz.---1m}. 54W Mata {1;} 01, u m :1: 1,1,...,'m. cm. maul. WM are/n13. 140$“:sz mammmammmmsmmw a1,u.A/w..u. T:S--R. Which, aWW finbwwas ucaLtuLaLmW. 15) Adab'five. Act mafia: Let T: s—vR. he. :1 Ad: W'm. Sf, fia¢aLLAfes,A,_es amL Amfil2 = cp, T(A,UA,_) = T{A1)+ 7mg), than. T WMms gaudwmwwmemmm. f6) Adm}; Dffl'miflcm, gt Pubalrt'lilfi": LétUbAab-imifi mm Apmm-SMMW M%U.Letmwmnfim P:5-rRAa.ti29-gm kgflmfir‘mg Mam: Asu'm 1: Fm. we»? A 65, PMJzo. Axiom. z: P(u)=1. Axiom 51%Ages MAZES WWW flw‘vfi W Ham PM1U32)=P(41}+P(62). mePmesmmmm am'am1,2cmd.3 Lamaphm'ugwbn and. b—mAes, P(A)i4cauLdmpwba1n'th§¢bueu£-A. Tm mm Lu,s,P) MMQPW‘W mm, 1O - 11. PROBABILITY MZ—T— 45' 1'7) Eflfl w W: Let U = {xtlxunuz'n} be. a mmm.afi P({z,}) = P({xz}) = = Pusan“, than, W125 {293, ixz},..-{zn} and. mum Wu? M. is) 19) Candiw : LnrAamdsthathMSJbaM WWUMMPmMpraMl/ngm Wms. 31, may”, mmm'm MM P(A!B)01,WA3£MMWBB 4W“ 5'1 PM n 5) P(s) 3'4; P(B)=O, PUHB) c.th ha P (MB) = 2.0) ngktmw: Le: Acqu 5 new war; Pm) 70 cond— Pm)”. atm. Mm P(AIB)0&WA3£M m. amt 5 i4 9% 12: PM), Lie, P(AIB)= PM), 1 mm W A and 5 m. m t: he Went. ' Shana/.17, P(BIA) = mg) am. W m m I candifim. Award? 4, Paula) = P(AJ.P(B), 111m - W A MBMAMIBMWW. 2.1) M041me EM: _ mmmxmw,mmmwm 22.) 1O - 11. PROBABILITY MZ— T—- 46 but W the. may: .91, tum W a} Wm, mtg, bm'hwr'a. Mdem amt W humanmm. Puma I'M» c6: Fm, Wu. W AhaZ Mat A3 M PfAU-a-O (:'=L2,3), at PMMAZ) = manual) P(A9_nA3) = P(A‘1JP(A3) P043 0A1) = P(53)P(A,) mm M A,,A,_amd A3 mm to £22. pawan Wm. WM; For; m wants A,, A213 M PMH >0 (fall’s), if Pu‘fnflz): “Adm/’2) P (Ann/i3) = 19042,) PMs) PMsn/h) = PMsJPMr) Mada Foam/12mg) = PM.) sz) HA5) than. M 51,191,143 m AaLattabe. Wit: MAW. RWVHMAAQIL: MUMQWWApamW'MMAW WW. AmWanwmu, x:U-+R, EMMA. amm'm. 2.5) waabifiig ddtnihufim gt Mm mum: Lar x:u-+R baa Wm mm.a¢w XMW W in W. Aa- {x,,x1,...,xn}wudu Ba Mata;— R.me.4uppa:z MxWMnMamel-M laminating Hag) = P(X=xi), .945 Panza, ;'=1,z.-.n TL Md, £P£1£J=1J mqumm 1:1 Hm), Mar-2), pom} is mm a. Maggy MM'Mm at £111. hauler». Mable. «11,,11,..., 2m} P (cab) + FLU) (2' Ma'omzz) Hm PUD) = 0. Tm P(¢UU) = PfiU) = z.) Tumour» 2: 94, A is w W, P(A')=1-—P(A). 1m Eve/nix A Mud. A’m MW excfluszve WAUA'=U.HW haywiwehme P(AUA') .-= PM) + PM') PMUA’) = P(U) =1 '. Pm) + PM’) =1 P(A’)=1-P(A). Aha, P(A)=1-P(A') $me5: AMBmevonxdamdAcBm PCB-A} = Pam—PM) amt Poms ms) Pica-oi; ufifimm AC5.111i5£dAhwnm the. VW ding/Lam below: Name A Md. B—A m 1 W e,sz em 5 MA. A U (Ea—A) = B P(B) = PM) + P(B-A) P(B-A) = H5) - PM) F02; W11.- B—A, PUB—A) a0 W m PMJS POE) Tm km. Acs, FUCHS. B-A F'fB). MM 1: F04, WA, OSP(A)S.1. Pmk: Can/:13; ¢CA and, ACU. 1O - 11. PROBABILITY Acne/Jpn? to axiom: PM) an, . 0 = PC4105: PU“) GM PINS: PUT) = 1. Hm, o :3. PM) 5 1. Cowmlzi mMfiWAMB Pmns’) = PM) — PMDB) Pmk:Ve/nm (flaw [31:12. MAME} P(AnB’) = PM) —« PcAna) 4)Th.w4m4: AWBW W,m P(F|U5) = PM) +P(B) — Pmns). PM: meabolre VWLdAhgémltidcfiefl/t M evmtd A W B—A cm. Mud/jg axcmaive Md. Au (BNA‘) = AUB P(AUB) = P(A) + PtBnA') ...(I') am 51m! .—. 5— (Ana) am (Ans) CB, Han/1’) = Pm) -— PMns) mm) Hm, b‘wm U) amd. (if), we We, P (HUB) = PM)+ Pas) — P(AnB) “Wm: %A,Bmcmw,fim PMUBUC) = Pm) +P(B) + P(c)-—P(AOE) -P(Bfl<:) —-P(an) + Pmnenc), 1O - 11. PROBABILITY Pm: Pmueuq: mesuo) = Pm) +P(Bch—P(Antauc)) = PM) +P(B) +P(c) -- Pmnc) _. P ( (Ame-)u (AncJ) ('.' Thwm 4 and acummm w a} .421: @MM). 2 PM) + NB) + Pk) — Hams) —-[P(An5) +PMnc) — Ptnnsncfl _ = Pm) + 9(5) + Pa.) —P(AnB)—P(Bnc)—P(Cflfi) +P£MBRC). ' (Note; Than/Luna 4 MA 5' til/LIZ. Mum and addifibn MW :1, pmmaq). 6) To WMWWWP(AIEJtMMaAa WykWApabiMWBuapmfiafl' tin—dim cm s. Péfl: (i) P(Ans) 2:0 a/ML P(B) :0 Pf/HB) = P(AnB-) 30 HS) (ii) 3% A=U, mm In? W41sz a1, PMIBJ, P(UIB) = Hun-5) Pub) ‘- .— HB) ‘ Pas) _ m6 4mm cutie-m. 2. a} panama? Wm. (Eff) 94, A, and. A?” cuuz. M411? mMue arm—E m5, bum by a} mam Wang, P (A'UAZIB) = PHANALMBJ Pffi) End MMMR m of Alt mm, (AgUAz)nB = (Ame) u (A2113) 10 -11. PROBABILITY MZ—T—SO 56mm WA1wndAzmmuiaA—Agrmduuve, M14156 3‘,an and. A105 aha, 0.140 WWI/gum- gave. Hanna, #3 comb»; 5 a} baafiabafigg PE(A,UA2)nBJ = PMmB) +P(A,_n5) Puma) + szna) Pm.) = PMNB) + szna) PUB) POE) 111m, mwmlig Wm M 416141-4112, P(A1UA2_IB) = P(A,)B) + HAL-LIB). Hence, mdih'md Adkfii'u m madam 5, '. P (AIUAl'B) = '7) PU-HB) = Harman/ma) =2- P(AnB):P(B)P(AlB) P(An5nc)= P(A).P(BlA).P(clAnB) "fluid i6 cal.de flu, We. 61;- whabigg’ , 8)Thuawm7: Bflu'M:Lu51mszaMfl “Mm MA. exhaustive manta. is Hag) m P(A|B;) b‘D’L i=1,z 0M. Em amt PtA)#=a, thaw. PB; PABE , P(B;IA) =~———(L-l—-—)——————-—-a L=1z P(B1)Ptmsn+ Ptazypmmz) ’ Punt: Bud Wham 61, making, P(B:IA) = PMnBU/PM) m _ Non], by Mia'me Ma qr Mmm; amt m a, i PIAOBH = NEOPMan was) ! PM) = PtfifJPUCHBf) + Ptfiszifllaz) (Hi) “Aim? am (if) and (M) in (i), we get P(Bi)P(AlE>{) _ Pam P041151) + Magma;ng Fob. than. wax—luau? WIFE- awd. Wm M B manpmmo ” 1' 3' Pm.) PUHEH) + P(Bz)P(AlBaJ + P(Ba)P(MBa) L': I, 2., 3. i=12 J "U A u: h V... l P(B.:IA)= 1O - 11. PROBABILITY MZ—T—51 9J711w4m6. LfltB'WBzLLMWVQQ/fld. WWW; W and. Had-1:0 amt PtBfl-fiu. otth MB,WBZ,W PM) = P(B,)P(AIB,) + Pth) Ptnlaz) FEE: Anew—3 121 MW ofimm, U=a,u32 amL m A: AnU=An(B,UBz) = (Ansdu (Anal), W Bid/MABsz Wm W, Kama:f and A032 am. my mail? Mam. Hm PM) : Paxan + PMnBz) . . . . .. (i) Atacama? 12; Mpflmfim Ma 01, Manng, P(An5,) = P(B,)P(A:B,), and. PIA/'52) = H152) PMlEaz) (ii) “Aim—3 M (if) in (i), we get PM) = P(B1)P(AJB,) + Pth)P(Ale) 1% W cm bi. WM km. ML trauma? er and. Wye W 6M grow: PM) -— PUB.) P(AIB,) + P(B;_)P(AIBZ) + P(33)P{A:33). As 5, MBZMLMAUj Wreamiwhaum’ue) Win-g Bf=B and 32:3: Idem unite. PM) = Na) PMIB) + P(B’) PMIB’) ...
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Mathematics%202%20-%20Theory%20Part%202 - 5-6. INDEFINITE...

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