,t^t- w.Jr,rt^tta)=u.L and p(AlB) =0.5,find:(1)p(,a,1 B,) ond (z)p(Ac nB(){Q2:rneprob.thotonintegrotedcirtuitchipwiIlhovede|ective",,n,---

'- - -ond the pro.b' thot it hos either one of t1'te two delects is o.o7 .whot is the prob. thot o newry monuloctured chip wi, hovs' : k)iior

"trn;ng a"Jrrt given thot it hos a rrock defect ?

!:.,(2)onlytwooIthefirstihreebutletsfiredarenotbIonks?-lQ4;nconsulling|irmrentscor5Iromthreeogencies,2o%fromogencYD,jo%from,n,n,,WSuppose thot 10% of the cors lrom D , 1?% ol the cors front E , ond 4% of the cors from F hove defective rires .---- -!l!!.,yL .rrc) -' A cor with gg:9 tires is rented by the firm , whot is the prob. tho,t this cor is not coming f ron ogency D ? .

Ql:c;ven rnr yotu*iirs;;l. 4; ------ ----.----

lind: (1) c

X: 0 I 21.p(x) : o.17 O.Zs C-0-13

J

c24

0.07(3) the C.D.F.

6o.o 1

ond

5o.03

F{x) ,Q1!, meoa ond the vorionce ol X {4)P(1ax<4).Q6: X is o continuous r-v- ,its p.d-f_ is qiven by .Find k . ,C. , .:) e). r1r _ zx) .y(s _ 3x)

<-rr@1y; +

,07 .1

<1,<2

;V

l. A-lv\' \

-t\l\=:

_-\L?= \ .\- ry\ T J,-,-_s_dr;.2 7 , ,'\-- ^t

Ain Shoms lJniversity _ Facutty of EngineeringPost- Graduoie; Communicatian & computer Engineering , Design ond production Engineering,Automotive Engineering , euolificotion ond CivilProbability & Stotistics (1)Morks : 20

Mid Term Exom

.il-\\

''1,!'i';ir';,:f:']r=J,'",'"Li'*^?,';os 'rinaidequB)' 6o'otB) ond y!1 cvn'1g:)7"n _.. Ar" A ond B independenteventi ? Whyt / '-t t" tv )

/ l/'

A"%r:ihe prob' ,nl,o:inrefiffi circuir chip wi, ,#*,*rri: -,)r, $;r? ^;;,rr,*, ,, -r,\J-//'! .-y:: ? crock d,efett i*W), ond the prob. thot it hos both det'ects,@rr,or is the pro,b. ihtot'-'- i;::':,:::'j::::::0,:l'1.y"!n",""' 4re]tn,! d:r:,E- . rbilrtv"rek];g-'

"",')l,ioon etching defect given thot it frosnolo crack defect ?

(hot this cor is corning t'rori ogency

Q5:Giuen the fottowin96.y$f , roncJom voriobteX: O 1

p(x): Oj7 O29?__

c - 0.13

rom oeencv E

eoft

GOOD LUCTC

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,L. nt, oy osi;q--;'tyVl;T,

ry service { in

lprovide sotithe prob. thof. Ift)=

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lM ohsen R.,"**F lil..l,or,,c.\ prodocf,.n

tf p(A)= 0.5, P(B)= 0.8, P(C)= 0.5, p(An B) * A.qB, p(CnC) = 0.3, p(B oC) = 0.BBqnd P(A n B n c) = a.z4 , curcurate the fofiowing prohabitities:

(r) p( mEUe ) ** I * P( 0 UB\lc) =6:.4Prfi rr B uc) = P(R) rPLB) tP(d : Pr6\qB) -flisfic) * P(BnL) +

(z) p(A nE) P(AnBr[t : o'6 r'o'?+o'tr)'-o' q8..s'3- *''](& +

; r-;.:'3: c un?) =t:-:-i :(3) P(A ueS

P(Fud) = 1- Pca lc) = 1 - o'3= c.?(4) P( Av c )

P(Auc) = 1- P(A) +P(Rnc) : I - e,61- c,3

P(A)- Ptt\nts) -(s) P(AlB)t \rtlu I *

PrnrB) = ll q,lgl(5) Plgl@nc)l

ptBl

PtB n(A^c))Pc q

^c)(7) Pl(A n c) n Bt = p( Ff

o. 2r*o.3

n L)-

f-f t

nC) =0.3- c 2+= c o6

(B) pr'r(A uc)r = p (Bt (ftuc-))

= &eY#,p,trls)ilI::?;i#Pffi3

Ptnuc) ,,, .r-,_::-

(g)p(AuEuf) - (]'6ro'"r-'--j--.i..-":---..--' ,-,'t'*::'-l'(rluB-uc)* J -'P(RnB nC)={-o"LLn - CI'?6 ,',r,rat l

(LA) Are A,E snd C independentevents?'-iiA n'Bi'; " .tE = Pi'Aip(R) +Oi Pqqrt)= a t'*;p.P,tB] PtS)-oPtRlc)- C.3: P(A)PCc) +@ i tI-.Y-o*ncu rr^\depexc\er\-r

;;a;;;;i.*;';G;;;;";;;';|;t;;:;';;;;;-;;;:-r,nrtLnr6T-HjF-l"E;ffi.itlpii;sr:-.and p{B4A)= t',!-r11!A[8,; - p'T* if -7;-(c'T*

c'2) + (c i ? o't+) '=@3'-..._._.."-._::ffi .:...."*e.*r-.s-"..:.1.i.*,.).,

!:_::::"jii::.:._1!.:::.::.:.:::-:.:: : i\('r I = r (2', -c))= rrnr*ana ," =f,r. *, -- ,"Given that ,r.!;r._, ,o < x

" , ;;:i.{;;,4

,ryi., e :;-:{rI ,,il;:';*; f1r= [ , ,

(z)r@)d),1'J x = l'l.o^ ry>: ,. l, \(3) ur*l-;x (,xr) d 7 = +" T+ i--o., =.' +

tf P{A)= 0.6, P(B)= 0.8, P(C): 0.5, P(AnB) : 0.48, P(AnC) : 0.3, p(BnC) : 0.Sgand P(AntsnC)=0.24 , calculatethefoltowingprobabitities

;{\(1) p( Autruc)= L Q({}\)EUc) .1- fi',rn'] lci * P(i) - t{'trig)- P(l1'" '

r i- _ (,-P(gir() r tr(,{n$,iO]: r-!o6+c,U *r-.S - c.48 _o"3- c,,-:g t-.:.2

= FtB)- ? i'i\ nG, f, f)'1 o V''- e4 - 6"'$J4* N

W(z) Pi(TiT)nrl

.a\

N*" '\.o' (e ptB l(A u c)l

/,Nts ?r't t'i j[ ]'

r(i.Lr )

tl I. ti ri.rq

= l-t.d/e(J

(4)p(AuBuc) = FGltr-,/\c) = I-P(AnBt'c) = f?,Jd

P{E:) +(.rqls.ij , bs*o'z)+\:J:1)

and vur(Z - 3x) : 3. V (X) =

iventhat f(x):-{= , -- <x<ot isqp.d.f.of X,then(7) ff = \ +=rJv = L :i/ J*,_- J I *Z' !' {''-d)/_l

(2) ltx =--"4

(3) F(x) =

@) P(X > 1) = \_I -) !+ _{,

A shipment of 120 burglor olarms contoinsl{thot are defective. tf S*pI:!S:SS!g:l:_ore randomly selected andshipped to a customer, find the prob. that the customer will get ot teast Ti*Z$'iiive alorms

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t12; \tCr)

,)

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i

-1,4+ ll.4;,t tt tt

*'1""--l**',,| - {'} |. ( 3'ruo x {c;

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