fle Jubpero y bes Qipendent ventoble, bo Hye au ind Jondent variables ctay we Shlain o fineas. Allan 9 tafe an N= ath +52% whieh is krowa as rrucbhip Le Uneox, Ate ntss iow quahien Te Jind ob, hha t9e tye Poe rtd Lrast Aquat A heme vse gk Hh rimal eyual Os JolDouns ! 2y = no + ben, + be Sho Shy = asa, +b ene A by SH Hr | Sx2y = A224 tS ee ft a aeyesslon plane of he Jum Y= fbn dhode Ido “How ee as "ofa ot fal ea gna ny Feu moved & “Ka dondge Of” goede tn | Bnate bos Sows Ia “glitbrenk of 990k km fs moved do walght 9 9, Ostan ce q Cres tg) Ciecien) tas f hs (go ° = (12 Le ho 9 i a0 qo } $4 oe [28 | 4% ie 136| ——— Solu. Given? Y= Bo + 1%, 4 Bars Normal a zy = npe +p =X) + fr Xo Suyy = pe Sy + Pisa? + 8. Say t Exsy =p Sra t fy SM Pa Saat mY yy 4 ics: Ibo 640 6 240 as 3 22 m2 33608 bE Ady 4.89 Ve ho 64 "og SEG 69 a PD 2:0 Yo 108 144 a4 [So A 34 08 3 AI®D. USE 272 S40 84 4 ae Ge 4 892-6 23-04 9-68 = NFS ASE | BH, = 18 SarU) Sy=o Siy-2906q en SH Day Sxu,> : =Q6 209 =1181-49 = 18:24 Spot Bp, tI p, = 740 1B Po +62bp, FAAP, = 28064 Ul Po + 2p, + 1697 Pr = USI 4 Bor 14: S6/ Pi = 86-109 Po =12-160 ot %, =3-4 Me HS T = [tl + Oo hse et | be Mile N= 159-58 Tt a Gatien floes o Y on A,X my from tor ppt(3G;) = 39-4 lees = (j)*= 24 i SH, Yip = OU m1 =o] sy 844 7 Sey ey ages Soba. y= pe + Bm 4 fae OS y > pe'4 Ps 4 ot Po Xa Sy = pla + oe) = Gm y-¥) = p, 200) Ba Fem Owkg = (nm yg) = py E0r%) Ce) tp 80%, SS 20-76 = 88-4 Bt 46 Po O44 = F-6P, + 84 By Bi = o'4 Bo =lS pom 7 Oi — Pe = Y - pit — pave | pa. = $S-2 = va fo Us(6-4) | Bo = 99-56 ea | js l= BAS6 + 0.4%) FISK.)classmate Unét = ont Date Probable el slily Reo: ‘ | ayy Random frperiment } An enpeurent wlieoh predues mor, than ont Cudoms — whtn perpoiraed under ame eondib'ong Sompl dpaset- Te Aer of aU for Thle outcomes oh Q _Aandor enberrtoaon fe known as [endl Apes denoted by 'S d Gent i Ang Subst oO} S Fe brown -as an tent metic iy A 6G. de Probability : det a Aandom exPerinert haa 1 ro. mutually — Lcbusive ually Lire etkoushyre. 7 Also’ Tub 'A! be an an! rt of fe given rerden expofiment such that ‘mo! obo uch opmes be pavourerble dp A Ten P(A) = noe, urble euteo =m Tetel no. of Otrtennes n Noté ; Li) Ay ony evint A i O€ Pla) &4 anol PCA) = 1 - PCH) eee explant QA TH Maron Youy 1 Rr ony d& euendke ARR! PCave) = pray Yece) — Plana) si} AA one mud enclufre i Plana) vo = PAVE) = pCAy+ F ved) i ee Auth Hak “ee euent A already pened Fen —~|pobof Bk diokd b , plem) —; {1 Hea Plaoay PiA)#0 p (A) asec sessed eee eee eee EEERTO on prada Pa) = PCB) Plana) = Prax P(e) eshte barton wy Random Vartables (onside, an expt of fowing 4 pate ef cod Tuc Simple space! g S = fan! ar, TH, 173 dapinaX= { Non Of beans) we xed 21 Foy * 7 x ah 12.4 3 ta untghe seal no. | eae a punch A v he. X-is a Jemnehiory Ute mrapy cathe seems ‘, | 4 | fe. called r0ndon vatable bey Thr rove] Acal nos Aniyned 40 Cael, pnbeone l | a m i enperinede “ut lenown ak raage al a vandpm vartable Aeecovole) ee lane denn _Vartablis ar jobless te “4d iy OFreute Rondom Vouabl (ORV) 1- TD te rar athe wardens vartatle tc date or ‘hfluile hen TL fe Old Bey [ | oor: Towing a ein fore > Nios Jonas aan head append tom X= fi Fs 4 eae i nal ——4 4Continuous Rowden Viet able Ceav ) 1 9) ~the van hordum ver, is wneountabl, injinile bre. oa bo an _interya) 0) real Sous “Hen it ts i 27- Continuous Ral ene vartebles Brobetit Distibubon of Bawden verfable a Ka fa a Halle lay be a dfscrete random vertable chen use can jind__POK= x1) = POX) PO =*2) = POG) - ake, Now we Atbrteen} Ayslem abcally the _rardem. vay. XQ teedtspending parchobé thes in G dab as follows. | — Vv x | % Me - ee PG | Ren Pot) Whi ol. te known as prob distibuben Es x R ik sakshes THe following 2 tendihong, | — WP) o (oo li) SOc) = 4 —__| ‘ ae ee hun, he | pretabtlivy 6) X= x; AW er fnckh'ons 5 et POR) Ni grenar ag =SPOj=eT dineled by P=) o Plu) ov PO). Prve ig it Aas es ce Jelleraing 2Doth, Anon [Pdf eet : eke [aE] Be 8 ie ton ah ae Conv) the ust Ane pistbily aM ssl: POx=ti) ty wh mig rhted of 2d; ob he. PCx=xi) P(%) -Sx ox 4S; P(v-6e Sn Z VEX cD) which is Brown oe PDP, it Adlbpies Yhe plowing A eondthions | — Woah ‘ }) Lo wm _ fire = 3 |S ee I “Gomulatine Deikibuton Binchon CCE) : Tp x is a_DRV hen P(x 2%) ele 7 Say ov FIX) js known gr COL ond #67 | _ dipined a3! FUG) = lx) = = A(x) | : ui) a CAV thon PLXEX;) — dincded | F(X) FO) tc Known as coh Qe anee difinad 0 FO) = Fl«) oo | [ Mean, Mean of a -ranclom vartabe KX fe 9 _ l _ (Emm. known 04 tts expectation bested 4 =.classmate RE] = fede af 5 CRY Voriente_: Vasiomee 8) a warden variable daredeol pO defined by 2 ©n= C[ (x E09)*] by © EA a= © (k=n)™) ot= SUCH) pe), th x is DRV x Fe ayy tae : 3 Sets OY T Nore. * oe alo be wren o4 | — oe = E(x )- feut ots Efe) — (1) the prob- mass uncon a4 aDRV is gin by t- pbo_= 4 mel 2 --- --- YBa 1 — ol 1) bbe even) bet fle multe 93) plt= even) = pws. ots - + = plea) + plr4) + peed +-~- = 4 + \ t1 t---- a 24 2s = 4 jue + [ty aryy24 ] 6 ae 4 (47 (a7 = = 1 1) = fy —| 2 Uy] [3] ba = ven) = lL) CS) a“Tepe r= Me Vg GA person fag toda Z balls ak jandam fer | Tine ene rooney =F J) : = i oc 4 whtle & 8rd bells Buk J €70 foi tach_unhile ball Weak ee f “Cree Jor as red Ball tate he ober Fino) hs__expeckabion Seln. ae Lab X — Amounk » 4 bs. to_p, para ~~ To be joe ex] ce ek oh won feos me EX [30 140 Fae I % a % Let bu) = Ge = 2 = 4 = pl2Reet) cl ' % + > “. pl) = xq = 424 = 4 _ pliasty) a WG iota > f on I pUsa)= 4G = 6 =Q = plead * 3 | | 2 at et) as 21. plu) * H.. bla) + 2%. Ke) cian eh riae ee +t Mow nae > = 2. E[x]= ie =E 131-426 — Lt fecka hou. dunt to be potdclassmate Date Pege Se 3 ctu In a Aus find _ he enpecled| nos ef tosses o|__cofn ik X >No o} tosses § extn HOOT Tr rrr tat wp be phd epee % Az! ty ME Secret 2 3 Gis. play = Vo pou) = Wen = V4 boflewty 1- ple) splay Ve | poa)= Vie, plis)= Ka EU) = ty + ORG + 3Ye Te Ft 0 Vor ie t Bleed Sot St o ptt aa GQ) the Prsbebiy Bit) 0 DRY A &* clad by b= Pre eee eat San ee STE PO) ) K 2K 2K BK KR Qe Teak Erad the hee of (Kp) POSE) gem Piece) plienad W) Mean L Vattance of X Soler, f) PHEO Vx = KO eee wed RSV SL a ee _ Kt 2K 40K 48k HEE RK™ OTK OE | —_| Soka Qk =| =O ___| Keel Vo =H bub KEO —__| ~ [K= Vio 7 a ere ae eee tee ete ttePreae) = Pe) + PD QE 49K = atk PURZE) = PL) + A) +P) a 0C4) t PS) = Keeper 1 - oe) = [of = 0-8} PUIEx $5) = P(xe0) = 0 -B/ (tit Mean & Vorance }— Mun = Ele) = Sxpl) Ca Kt M24 TK +4 Ske TK HK MY Aq Ko 4 9K = BK + 6EK* ADK = 66k 430K = 0.66 +3 Mean = 83:6C Vorulnee = = ara) — (ea) ™ Elbe) = arpln) = Kt Awa Lute. 3K pase’ F $6 ake + 49. 4e-tu) = ROK + AB K + Q9K™ +83 at 440 kK * 4k AA + 12-4 = 16% —— W ‘classmate Dote___— ’ —_ vat : tient Te PDE of a -randorn vartoble X Ss given by me OQ = yoe ot ee ‘Yn BO" =f $09 dp} e: => fre a ee aa Syl [ea ae =] oie ee Sys [ A+O0 + Saree A TS CULT!LULLUW = Rye =. (ye = Vo) fi) * Maca gine p— v ae . Mean = €(X]} =" ‘% = “(xy e@ de mye Poe de + x oo oc 4 =f fag tna fps eet | pret a rs i= S ye Pe fey + arf — (1-0) tfosotte Dye fatter )y = Le) | Mean =o. ann ek] (ia]_Vowence ee at “ee eT = (ERD Grady ¢ Of) @ =o a7) dn - Yo edn 7 a wl = y [ee = Te JS : _* af f-t & Gi + 2 it ) a ° 3 (0- 0-22 = ffo-o +2 —([0 -0 +0 +] ocorerl a 1 pate =e | Var) = 3-8 = 2 =A wan en variable & has ‘Ta disihy Jn gin by pe 7 ~ eo cn ser Jena g J) = he ae Tk) pose) r= a fi 360 S 3 Te =o Kao = A =. i = dn oo= = «f ten 2k [Yen'n | =! ; 5S «xilm- (172) ) =) CK = fe 4) x_J im pCx>o) 7 ae =f tejdn = KL an . a tat = F = =k [fe x). = K[ _-° ) = ke 7 oe bE | 6 cauginous RYU is grisen by }— DE Bx> it Of ne nah a Rb suc Mi) plisa)= plea) i) plore = 0.05 —_Seln» 2 ee— (ii) he —APanurtion penrb) = [ [694% | a ee ees a ! ea I Bn dn = SP Bxb an ae & o = iia [ ey, = 1-63 = Go l=b2 = iD.0 Ss ota b> =0qs ‘ ae es) (P| “BVT olfameter of an thohie” tably is eraomad ne am a CRV usith PDF: — ae di) = kx Ct-x) 0 exe 4 ot KO find ee ii) Rad mean oe [hii) fad vournee “4 | Sly. []] ~ jeans x ' a 2 = pagina nnyclassmate. Page Ela) = Papodan ° = vz Kx dn _ SK TG dn an eo ee “3 wot saa Ele CaeE loudest EL #™) = MN Yoda 2. ak!f (tn) da = K Ca NESE ae Kl wt oe as =e = a = Os f 2 = 08 oI = ddsPvE By a (3, UV wnet f= | 0 y Ener Za-ax 7 £x£3 Oo oturwite = Find! = — WL a - (i Cor 4 x Wn" f Badu a * "Te: ~o54) der] —> aE + a eax ey] = ee ee a 4at Si-4Sa=} ; a = 4: Sa = a= Al ————— Gil cpp :~ Flo) = p(x ex) : =e Hada cf : i = a ee th," yan te Sens} fx) =e + 3.2 dbo ol 8. Tt rs ™ interval (4245 Fas lial eee zi aS —>) Date classmate Page f(r) = e+ [ag de 2s. Ta dx ° i ia | Las Ot aed Qh 25 7 area : as = Qn™ 4 2m ~ 2 peda sy Bi et ( Fie an 44 la 9 [ise 14 Dees Societe Ect tm mierwal ? Bom ota eo = frye fe Ae r tes otf Bans 7 dos 4 ea W ° 4 b 4 Ve oo ly YI "Ua —2%..du a3 Tt (lL fod= = g m23i- fae 45 ° f Te 4a : ( O_, «£0 aren EC) au 273 bens BY eee 6n-n™ ZLne ENshow ea DAV tolled” mole Dp.g sa ti “lid fort 4 she dishtbibion where: n> no-o} Frals_ b > Mob of swears tn each Bod. - ge top wt fib ep atl. Ns eath -beal =” The ae PME flex! the probability Pa fa Aulteys suk eho ime of tals wary | a] nl = oer 3 @yr fe a Seat een - ~ 3/72) + a! paar : nian) pees i Ay 1 = nb. + nf) 5 ; bg = Pa! + nts) rae BE eee raat : 2Ln3 apie ake te ude tf a abd 7 Cah = Vanfance : = FT ERIE eel : =e Es n-X = oS tt er eo aa 3 = 2 [Ge <1) to) com Pees 2go n+ > = 2 | zev-a) ae ie dest sing tt Hem, Ts + :

prob. of _man will One Upto Jo t we8 Siig ta secre : ae ect SAS a my =10. ere ve = PrP t—3 a aoe poo) = ey pe gh Me O41, 2 ---L0 an plas "cy [o-3)" (0.3) ee . nae p(2ecr = ple) + pC) +B) + BID + plte = te oa 0.3) fhe tee % 4G CMOS) GE (09> = AH0K GD9S x10! + Ip (22%35K0 ) + 4S KS 1999 Y103 4 1D x Os0ID] “+ (=X) ©0282 = Ooo} +2663 +0:293y 4 0-1} qoobe 4 pabcie sag {Mt Saratgoo pene wstth 5: cATdasin oh Z how aaa Jonata apould. be zncpected. to Rave! = Bb 3 3 gids ny 2 boys On 3 boys Gh Given 17 5 children —+ prob. } a My in @ penal = ye na) > PMPs a pod =" p 9 7 | - et frre 7 neh nes 5} pecado_t — pea) te = Sex (hy (a) : : Are aa k FE ulin = uk a} B60 deol =(Sye Ee ote is zo Yeo Tie =[ O52 | Ww) pO) r= SCo Cy)" (ee : lo x Va * Ve See _ Ss S - i of tye Iba ) [+3 ; ew Roy. Sdyhion = cut Seo Jondlies sapecbed m2 pote favtes S Bogs ae! * = Beox S/i¢ “Cosa eee ee eet| fi) pO) + p) = pred) 5 4_& i We 1 = Se Rope nes dp jamibes = np = Boor S - = Soo ; (eld CG) Deo of Io betes “an _unblasesl tafn ih Anus Tony oses Con, Wwe ¢: eck Hi) le . Sanaa n=1o poh gave — rob + heads ny fog : Pane f= - Gea [pee) =e Bp as ui We! j * (ny * = : i) pla) = es eT Ee — = “lio = x |} RK | De ee I = Is zd + Noe Cases = a f lo of aah my (0 Ath: [Bae = $95 & 1-97 Br | XC sels J22a classmate; eee = —$ oe 2 ag a By 3 BST a, Tala [etsy 45% 1 t Jo x4 aes oe 1 118 24 7024 Loree ©=—84 Ta 1% Se) a ‘ —T 4 : 4a. fate ‘ 1 Rep ne: Couey = (00 Vey “fet = (9-18 & 19. ebs" > tT + 7 TW no iY dete p Rone Cones ma Ode or Ame Few brnomdal vortate sith frre bates sy 6-2 Ty lo Grea ant chosen at rendem atiany fhatank ea Ame | Ken Jind prrobobinity —Kad ! CU) 3 aw are 7 ; (WY Atos 2 Gres i yi Afmoce 3 Uncen Oe loud : : \ Pf Z =p =_ b. oy A Ler prone Line bus boo ar 3 6B — 7 “= |o PME ee pC) = a me = =e 7 ae Daa “=n ++, 10 . =rf = prob: a hi - st + pti) EI pa) ms Te Oy. a CEES . = 0: 30lt89 ; TS 010739 + 026943 = 0/39 + 0 80/989 + 9 2°/ _fetssen Dishibutern the probarbilthy Ashi budoy pe Sees 1 Qiven reba plat) 7 -— nA ae ction pad. ikea t 3s_brown ae oe Tea ease vortate A_5. a> constankt vealed Povamute se i = | Mean = ET] = poy) : 2B wer 3 at TT , = < eA (QH))J Fa = eo A 2 (tean = A\ Notaner = ECC] —(ERI)™ Cons} dea }~ et kN i hove Efur) = 2 x? ply) : = = febean) poy = = but) bn) 4 Z plo) ¢ = e[aeDe d= 1a A. ce -3 eS) +AYe vale of 12 Js, Prob. ol ramsmtaton roy > $s 0-001 Jor cock us, impale rab. “that 2 i) no Crnor_durrrq a HS i) J ror during us : Ti) gXeasp 1 Ord, " ” iv) albmpit keo “ ” Sin Betg i “Given | pes. of Arr! _ p= Ooot a2 ener, > ! n Note : A N e o bmi ts + bol) = T a aoe ea a) Rp probe = Hal toe 6 as at ——= 5 =e) 4p) +P@Oe classmate S Date _ Page ____— = 048809 40 ONG + eC = (2 1212) 2 ze 0-9a9G4 — On an average D0 RAC, ane found ma _jinsol volume blood Jey a normal _peuon . DefeamPnie the prob - sade Hs. blood comple of (& novmal ppeison wot! tentain !— (1) lon han 18 ROCs T)_mow “an 16 ROCs — = — FJiven |-— PMEI- pO) = os 20% T 2 i) hep. pre pixcis) 2 = RG = pl TSP) Kee ] = pW POs + pay oe Te [a at + 207 + Cie St 4) ob aoe es “ae 7