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ane ( -PROBA no. of favorable outcomes epe- De nis) a e PH= Total no. of outcomes Example + & dice is thrown Sample spacels) =f4,2.3,4,5,6} Event A): Event of div. by 3 3R=f3,6} Oqe aed 3 Event (@):- Event of obt. on evenno 5 0=f,4,0] Oyo bad Eventlauey:- A=fch = f2.4.6} ave=fra.ct Plavey= 9 Aves — 4 = a ng) ac % Mutually Exhaustive event!- 20% move event are mutusly exhaustive if Ahete union gives Sample space. Gi a= f.4,6} doe = fa2.3.4 sch 4 oa eves * Mutually exclusive event:- above ex:- gnc ={ | 4 sek @ [PCaug = Pods ec@)- PCangy| fae A=B6) O=fo4.c} > e(auwy= & Eg Rolling of dices ‘- dice > Gcases § 1,2,3,4,5 sch ty dicelS cP cases Adice sch » oA ‘ Pace. (4515, 1C ar <2E23 a4 as 26 > 26 a1 3a & “24 35 36 AY 42 43.445 4s 46 ap Bee Se S483 56 gi 62 64 G4 6S ECs eum of 2 dices:- 2346 64 29 10 12 cel 23456543 2 4 (@) Two dice are rolled ase W) Pfsum=4 ens] = aes 2 ty ™ 4 (id Pfiurm is divisible 4] =ft,.8,n} > ust, % Guid e( Prod. is 12.) = (29) (6, Sans 2 a Gv) Pisum is neithes ¢ nox al > eee aan) 33 == 4 (Single card 1s dxawn fom 6 pack of 2 {5 PUicing ory Ace’ > ins tid P [Keo Heath] 3 eer cs = 16 Sih (@} Woo card ase tie ae & pack of Si casds ti) P{both king] 5 Aca $207, (ipelone A AonekI 3 40x40 Sic, 4F Conditional probabikity '- Soe RD PO OS OIA ie bu- A fait dice tossed once. What ig the prob. of oblai ning ey given that an even no. has a 3 tren no. occured = p. 4, 6k P(e) = Reale ;- Total case = Sk, 5 multiplication |eCr =? P (A/a) = tipication [Penney = Pte) €Ve) = erm xP e Rey = = elAng) cay + Independent fvent!- Tt AZB axe independent event then - WPM) = PLA WD PLameed}=P{Ad- Per) o, } Gh PS)= le) 1) PLAF IR) = PLAED- PCA GiiyeCAng) = PLAY Pew) PLAFN RS) = Play: PLES) 4 Bayels +h:- [re>= Plane rns)s6(es06) Total tie: Theoxer [pay Pa): PLS + (Aa): PR + Play (Ma) | Statistics 5 fox the set of dat fa.sa.q, 2.6 find eae SO = 346 GD median = a > 2a (iii) Mode= 3 uy Range = © P(A) = come 6+ Se =S hight lowest W) Wosiqnee =(6*) = g xi- ML i=) on Sata (BY 4 (2-1 B= V1) DIT a € Sos 2-4q22 Widest deviationfe) = [variance =[2-4922 SUMIT KR” Disevet Random yariable Continous Rand, var. y v Counted value infinite value Exi= A paiv coin istossed once Ex! Duration of call Ki no. of heads k= par} Prob. mags {9 Om): ~ | Use ter disexete AN ! x = [0.00] ftob density £9 fly t- yse for continuous Rev G) PED do | & £00 20 ae Gi) POU =4 , &b F foo = — — i WD PGO= Pex) | Gd Fry = Fan die is loaded ge that pvob- of getting face x is PIOp. to 2. The prob of an odd no. Sccusing when the die is solled would be- > PoosEe PUensowvs) ePOV= 1 KIDE4QKLAK SEK SRS L 34] PLAy+ P12) +P(S) A SA ade hes = Fay Pts) 4P(M=2) 40(4=3) + P(u=4) + e(U=9)+ Pluce) 24 it (g) find the value of A such that fun £0) is valid Pxob. density fn fu = AL-1 (1-1 for Leuca) =o othei wise. 5 ao Lao 2 > } foo=13 (fobdus (fe dut( fopdu = § fs Sins Froosu (tyfa =a aL > iS A(zuu*t44) <4 3 Az & Ary 4 FF Expectation tid Expected value of RV 1 is definedas— Euecay, when x is disccete tandorm vqriable Loy joe {sfdw when at is emtinusus Ran. vatigh: — (ii) Expected value of Rv u? is defined as - ex POO when uw viscret Rv FOO] ee Flag ae when at is cant: A oO Gy) Variance = [ey] cp ef ean > Eads ut Gp E{autb}= a tists W)vatiane of c= O @tel=¢ KI No- of coll dys. innan + Binomial diskai bution Se The prob. mass fn of Bin. dish is given oy — PLU = Nevravtgn-4] 92> No of trail | \ cxlP) ay i U> No- of times event(A) happ P> Pub. of event A is Single trail: Ls 4 -~B(P.a)| u-follow Qin: dist with parametes P£Q then - MEAN =NP Variance NPQ Mean = Elt) = eA) yasiance = EOY)—u* =ex e() (@)A epin is tossed 6 times — (ay Pfgetting exactly 2H] () Plgetting atleast 24] TH 9 manufacturing plank, the piob- of makin 9 defective bolbisot. The mean ¢ standaxd deviation of Bolts in a total of goo bolts qre respectively. 3 N= Goo meqn =Np = Gookoi= go eS ae = stand.dey. = [Variance =fApq” POS Seeds 3. fa0oKo1Kog = 3 (8) A fais coin is tossed independently 4 tines. The prob. of event “the no. cf times heads Shou Up 1S tore than the no- of times tails show up ly — 3 Ana 5 + Poissonls distsibudion = special case of Bin. dist. Gd 4S, Pessienls dist. Nee (no of possibility =n) = (et3) Total no. Ps Very -Jery small x= PDO) i Tis Pmf is = STAN We O,1,2 --- Mean =A vatiance =) (@) The no: of accidents oceusting in & month fallow pois. dist With mean gs §.2.The prob. of occurence of less than 2 accidents in the plant dusing q randomly selected month ds - 3 plier) = Ploye PCD 3 PMPs cate at = cs Wey ze is estimated that the arg. no. ot events ducing ao year is thyee-What is the prob of occurcence of nok more than a events over q 2 yea dusation? Assume that the no- of event follow poisson dist. > AzBfyt Aack = C/ayeas re io Set > Plusr) = Pt + PL) +91) > — Sey ss SS 0-034 Any a SUMTT e 3 ooeL An 
