Probability and Statistics Formulas, Lecture notes of Probability and Statistics

Download Probability and Statistics Formulas and more Lecture notes Probability and Statistics in PDF only on Docsity! | Scanned by CamScanner xX am XN Date, Page No. | an are 2 RV +hen Or, ©) xy +eaXo xX Ma’ ave ate RV @ e » | piste Lvwne. | let X be a. RV depine fo att veal (9) pe, ECO = Prva) | cadet. cuistrt brite pire? 2 RV CX) The aisivfbutive June” p ip alse cabled. comaouutotive | nludteetbeataor fare.” ¥. co PLX<% : “f | Propertuba of Ot Dieter Cbution fume” il Pp (ac x<b) = PCE) - Pla) DE a Avix) ond @ <b) then* e(-) = Um plaro w= F() = We FCW s) W300 |_| le|_\el BAA ES Mean _Vaxtance 2 Standnasich Dewi tien Mean Wu= € pha? — = pin’ 2 PEPE ELT os Ept (xl— uy” 8p 2 feta — Scanned by CamScanner Utnialt ave independent §gimlly psa ove foal F conshn) | a | Mean $ vavtance at RD '- | Ls Mean oe, astrtbution Ut mp | q | x Vouaree (<7) = np 4 | _ > iz 4 8-D Ce)oal ppg I a | Re cuuryence. foumula ef qne a nr Prolo- oy btronual, a 5 , ET = sh} bidiega ny, arn) cy | ) (n- al : | Wek plyd=n ph 4 = ih b Crery) x p(vt) sh brtag™” rt ert oct Cn-¥)) ~~) pb. Cr-r) (ner=5] Ll pl? hv), teeny rae S| sal” Scanned by CamScanner 4 Port) ne wb ptr) eb Vv =) |Plr+i) =fner'h re \ set) | — F yr) Yd | | mapas 6 oS 9 mean, “eps 6 0 voviane pe © es 4 7 1 Suter 4 preb: of fol luve udttuich Cannot &Xcees dhe wefalae o an SI Asuéttad 12 getttha {17 oor. (6) BLL evel) De die Lp tow tne. - Ell the mean $ vauda wet Ob the no. my SiLet éxadh mean = yp 3xYy =) —| — Vavfance = npys WK ex 9) weal = 2, , Scanned by CamScanner | a o Gol lety po ARV choosing the noo a 6 ec _ I ba I here ynsio . ps lo/iso =the ao i ’ 4, f & S| REX=1) < © C¥ 0) C3 /0)" : I = 0 :2974 (#5 p(vee) = tee, (fio)? (4/10) ® I =_ 06-3496 feral POX <2) + Plxso0) + P(x =t) + P( x22) I = 60-9294 | I i Que? | 6 wth emia. Vassote (x) hades the relation IP(x=y4) = Wr1) i Lmhen n=6+ [inc the vatue rf the pavameter {9 and x1) Af, pq ye &, pat ge p> = 6g? Cu r Oy v TS SPyq2= 6h, Wx 21 Uhxzt Pla, = My 25 Poaa] = p+yst fo, x4 sy Ug Jo =! In Sy a » LP= Ya] ee Scanned by CamScanner Date. Page No. _ lt ect rn yt =O 2) 28. suv p ennalennheninnberasnsthensiihesissiheatasilesasinninnnaisiansiitli \ | \ a — tt Gz 1-0-3u | [q_= 0-68] Nl: igo 7 } s t . Wiss the bihamiak ditstyPbutien Niq+p)” 7 =1S0( Poy py gn) 3 Vv j | = 1S oC Mer (0-82)* Co-ed ¥] , = { ch dor =O 1S0 XY4e, X(0-32)%x (0-6Q)4 = 32 -0% | iS ex vets t8o% Uy x to-a2)' w(0-G8)>= 65.3% fad fer 722 3) IS0x Yes x o+32)*% Coreg) *= 42-6 ti») fa ve3 = 150% Yea x lo- 22)3x (0:68). 12°3¢ WW) ox F24 a) ISO K4eLy fo:32)4 x fog? = 1 OF 0 = Guts 4 the. _prebabiity oy hfuing a target iS lof, and lo shots are fred : 03 Le thet the target will be hd atleast ane? op Nain L 2 p= fel y go ie a tall t6 = He, eCX%z1)s 1- Keeo) eta ec, (yd C10) '8 % 1-(9fyq) '% =_0:68/3 Scanned by CamScanner ae Qua, Ortlra vt. bboy — ae = UY ane gfe v ane sty Ob giwls_. Trott foe bays gaace, | -Asstumeequat.prabaniti'te for “ cou Na+ &) we atin ¥-eatleleea 22th,» ~S \ Pah 04 So0.faanel \ “ldo es usouta be—expectets a — 2 boigs fod — eS — 9.2 Ufo pL PCx a2) 2 Ue) C2) CY) VW uxs » (494 > ” % «CV2)% OBS v Ne- on families = 960 XO-SIT XY J = 360 PCx>1) © | ~ Plyso) sto Ye, Ce) Cn) 4 = tL={ Y,)4 = 1-0-0620 =O. 9a3y e: eL. fantl e « B80 » agar . a) een 4 Scanned by CamScanner re Date. — Page No... ———=— —— — mreserromenren wees PlX>2) = PUXE2) + Plysa) + Prey) a -y y, Une (AY! 1 OL Hs) CH) Yes CM)? Ce) tel Aye _ Sy Fe Ue (YN oly" a = O'6QET fe | a I - oo NO: Of Jayitits = OS XO + S87S T — | * = S50 — | — | 6 fue! Six _dutin ave thrown 729 dime ~ Horo many timéa, ott expect é p_ 283) Fe" | . $00.)|| Assuming that en-the. average ene telephtne na —— og Jo T i Ort 4 iss cated b/u) 2+8 2pm on week aa ys te Susy: what 4 the pretest lily that 4 6 randomly selected np are catled (|| net move then 3 C 0-499) to) | atleast 3 t o-09f) Sf. tnem usizve be busi 9 Scanned by CamScanner Date. - Page No. Asie tac the patnbiley %. succes coal. mther teDLead Kaw wa. rn OACOhe rE Alt thad Gar. by 0% j—<k2. UO Uke. poviéden ofl outlon te saLeutate. Ahab —preblandatltty bhatt. employing — 2.60nichens These wb -be.octleast one fatab occitent.' Tae ype —Carfven P= /eu6 dnd ns 260 =) As nig s 26/2460. Az 9/083, Snipe Maids a (ed PCR A) 2 6 ar 7% 15.oa3)7 } vs orp PCX Sey. pew x0) y be [97008] wu Oo 2 Buppooe. thet a book a 66D poqreceivtalins ue parting mister pas asatame that there erretta are. eandanides,———_ MUetirfhisted taabeig habit the book and (ir) = ma. ey OSCE ? ° | poeu. page has a. povrtvow alistes bist ona L2het 13 the pryeb tat lo pagea Setected. pt rxcandena uilh be free pNem errors. MN =1o p = Vole = 1) a T TTS Aztinp = lO x Yate fA = O68F] == PCxeo) > eo SF yew? ol 2 HO’ e at sod! Scanned by CamScanner wrequertito (260) °°’ (os) = Cla} 366) (0-5 121306 bo 6X3 [x16 DF 0-80 Scanned by CamScanner Date. Page No, The. 2 tote tontinupuc olit usnoae. _genessabe0g”. ~ fO% the. otha pivea Pp — sem mesnerenterapemranpunieineanennsiamirete ne 4 (as ts Bo = — —=th- section —J _Wheue the. Vetcoble su tonttoumea all tie. Walt le enn lf ta O te oo ee einen ——— Ap Outi tne Cute, etesta..o4- Ne. oll eeett er | The ranctom valuable Aenea fp? ttorseo ND ta tleeks.... |} jpetenaad variate repriaenitect ty te Dey) fn soe oO Licopetetiioa Of netemaL ates ty eh BI Fo n ° “no, ©, * 4 £q O14 tetheel ne Prbbabt bitty emettes ferne- berhuich fete erste the pot lousing ppt Leperitite Coll pee) BO —— & oe . — — (tl C eearee = — ype ° (HO || the wep Sypmnreeticue: ober t Cb mec ae Loy) The mean median meote mpthe M9 tadnesills. v . 2p. X18, 2 noumal vourate wertn the nocorm(stjancdk. Spee) , use aOR telat fiQo the ND tiwth Abo $=] Scanned by CamScanner Latins bo -te pt Yah eb st When. 1 ke tole eae 3 When e=sty, ¢ = luo = 2 , 3] Plog xziyy: &P(o < #4 O64) = ax [bce~ 6-25) - =-« O:4UF Scanned by CamScanner PCWexK<tS)e P/o.g Z ony L = Plocx eo) + Ploteen yy © - 2001+ O-1SSY ‘a O4uyas PC x76) = PCR >1% 2o-S-Plo < ALG) oo = OUND Oos UO Scanned by CamScanner al Date, — Page No, _ a i | 1 T : ; : Sue Ama upd rer -harariea fyb} hata peta, |S M the reofcta new ee the yeaittOr1e. Ae / Metumnal. ueth mean = pep BIAD 2 . (e2rhas Plo — ep Teo ts ui have reskta i FO - tor & so? dk =1060 - 22 . lwhenxX= 98 > X= W-160 —2/o. oSal 2 = X= lor >. x = (02-16 t2f/2 =] = a P(98< x< 102) = ePlo< z<1) a 2 =x © +3423 = 0:6826 68-26 x oe es StOsr0o st $e st Will have resistance iw b Ju 4 =/o- Scanned by CamScanner ¥| The fist: & mements tthe Atetribution ob est Ie pea » ° oe Oo vero ble, ote, 4 -4o Sham that the mean a, — e Vasrfante tof and sin ta - &% , 4 Cofiien Voltito are memenk about cunbiary am 2 | A ' fe Mlet, daoleig | ywate-vo Ay!= %-A be @-2 we = 2 Me = bye Uw! Aye Mal - S42! +2 4’ ~ euoe BxIG KI +EDKIF = -Uo- Ue+2 Ady, 2 - 84 D_ayork Ve retvo b. mroment Que) fa Peitote, “Hhes attance, and snind c3e tyrem the: Lobleroing olata - ue fee lol i213 G@ ls te |7]8 lat (| 2 lee! 59 qo (52 aia / ! ge! — le E phe eA Fu fu* 4u® b { -y Asti Atuy Wy Ie —6y ! g -3 -l> 8) -2y2 p 26 -2 -S2 toy -309 > <9 =f -s4 sy ~<4 Y 72 °o 3° ° oO Ss x2 ' SL oc 2 L rT z se 114 Qb2 L + 3 4 63 <4 Fese + u GY ° ran SE oF BRITE BG Scanned by CamScanner Dato, _ Page No, - ™ . ae = \ 4,20 ao = Lg! - Lyl ® = 11-9808 — (4.4% xI074) 21> 980oL — 0. 000F UY ol Vt + a Aly = dy! - atti! 4y/ +240! uw \\ =o: IWHS a 9x1 7797 xf =0:02184) 4 25 (9.01950) ~o-l4UYs +S: 9 392 X0-02434 FI@Axe¢ ~o-luus #O-1623 - 2x (0:0. FAY)S =2-0a9ay)$ L L Scanned by CamScanner Date. Page No... nla ey ine cUstrPbution about dhe. ae he ~ 80 One Lo8 tnd the ee and A. rooms ° ! 1 2 3 4 § 6 + @ 8@ 2@ $6 To $6 2R BF | % 4 Scanned by CamScanner Cine o¢ x<I r 2 ig, | | i 7 : —« 2K -K F If- 9k mel re \ >t it + +k) Fs+é H 36K 4 [9K +UK = = : = - tH sent iep Sa MEE ae Fo Te K he Xen f SCIN = | ea 2<%e3 E i lL oo elsewhere _ WT Ftind K UD PvE 2) ni, I - $ | oh f4eude yf hades fdet T (aR %+At ) dt? i ~ oo : 2 r i ! i Pica]! + Thu] + Fee? 4 aoc] & 21 i La fo - Kee] h Scanned by CamScanner Scanned by CamScanner Of LEC, CPO Scanned by CamScanner