P(E, IB) -= PC B I G-~ f(Bjf,JP(e ~P(13IE..l-r(E~...

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r , B ;:; f(Bj r=,)ftE.) 5 P(E, I B) -= PC B I El ) reE,) )( G-~ bay~~1 f(Bjf,JP(e ~P(13IE..l-r(E~ +"+f(BI) TheO("~WL To-b:J, pro ba.b i/i ~l "'ul e, ~ SuFP()~ PeAlS) ==-0 7 V'inct ph?~q,b~ht-.Y of P(I3IA) ~ ? f(~IA-)= ~== (O'T~{OIZ) == 0,2.8 Pr. ) (:> Ctulf-t. So("e. w"t4h ov.f !;..et(\d ~W.eA ~ 5Uflpo~ P(ItIB):= O.If/ P(AIB')= g-" fa}) = 0,& / firx:J P(s/A)::? P(~tA)-:::1{dJGJf(li2. ~ elAtB) f(6) -= O,i./2(Q.~) -::: 0.81 r{,+) f{AIB)P(e,)t fCAi 6' XY6') (O·lI){O·S)+ (O.2,)(O.2) bx'lMM~1{ tt.:l. - ~ r (~(},y£s I ~~) f(~dt'wti~lSO~VO·nititl~~) -= D.Q1 p~SI1:l",t === r(stD) P( ,d.ut;bl~l S'~ vJ/o 11I~) -;::.. ().QS ~G\.+l\/{,::::' res't D') --nu.. 'rtci~u. c~ +Ju...-1l1 ~ It-1. tJu.. ~ fOpt-tlaft()¥l : O. DeDI 'fou -tnu. ~ tut t»'la -flu.. (.esu.l~ is fosi-t1~, rC}tnt h6.V€ W~)? lu- D: 11u.- WevrA- ~l,t ~.e.. ~'U.- illf1.l.V) S :~ wW\%' +h-t tv>t 9L~;UtI is poSi.flve. . G~"fWL lid: P(DIS)= f(SID) prO) ~ P(Slt)- 0.05 P{S) foS',+i"~ tl/>T wl-thowt-ill~ = pes l D) Pe D) «().qcU(o .00012 - 0 ') - o o~ f[~ID) fCD) + P(slli )f(pl} (O.ffq)(O.006J)+ (o. 05){ 1- o.oot) -rcf .. h~YUA1 ~,l L5 J,l3 -1 ~, 146 R.l48 5epi 'a5" :)j)l~ :\\=~.ll5 ~ 9~ PN 5LtU-eS5 ro-fe -ni. (Z7~~5~) 9.3'/. ( z~Cf/~o) ~mAA. 5~n..e.. Cl?' /. (~,/ <61) iY/ (c34/ z70 ) la,~ SP,ru, 13·j. (IQZj263) 6qj. (s5/~ J P~vvaAlfttl 0.5) = ~!f' i:: +~ , J10 = 0.18 f(ov~ ~ PW) =~ ~-!fo + ~~, JI~ := g3 \~ StAtiFiJ SlACU--SS .fu:lllAf"e.. 5;~i<.. [~ S~ lOll. 9-1 263 SYf\OJ I c-\oYl--<- 'if I 6 1/ 1 f(lr) z: 0.5 P(8) = 0.2.

Transcript of P(E, IB) -= PC B I G-~ f(Bjf,JP(e ~P(13IE..l-r(E~...

Page 1: P(E, IB) -= PC B I G-~ f(Bjf,JP(e ~P(13IE..l-r(E~ TheO(~WLroneducate.weebly.com/uploads/6/2/3/8/6238184/engg... · ~::: 0 'i1.i«,1I l (I'IDtke4 x,.={1 C-o((v-tly If ) ~:::l:t If

r , B ;:; f(Bj r=,)ftE.) 5P(E, IB) -= PC B IEl ) reE,) )( G-~ bay~~1

f(Bjf,JP(e ~P(13IE..l-r(E~ +"+f(BI) TheO("~WLTo-b:J, pro ba.b i/i ~l"'ul e,

~ SuFP()~ PeAlS) ==-0·7V'inct ph?~q,b~ht-.Y of P(I3IA) ~ ?

f(~IA-)= ~== (O'T~{OIZ) == 0,2.8Pr. ) (:> Ctulf-t. So("e. w"t4h ov.f !;..et(\d ~W.eA

~ 5Uflpo~ P(ItIB):= O.If/ P(AIB')= g-" fa}) = 0,& / firx:J P(s/A)::?P(~tA)-:::1{dJGJf(li2. ~ elAtB) f(6) -= O,i./2(Q.~) -::: 0.81

r{,+) f{AIB)P(e,)t fCAi 6' XY6') (O·lI){O·S)+ (O.2,)(O.2)

bx'lMM~1{ tt.:l. - ~r (~(},y£sI ~~)

f(~dt'wti~lSO~VO·nititl~~) -= D.Q1 p~SI1:l",t === r(stD)P( ,d.ut;bl~l S'~ vJ/o 11I~) -;::.. ().QS ~G\.+l\/{,::::' res't D')

--nu.. 'rtci~u. c~ +Ju...-1l1 ~ It-1. tJu.. ~ fOpt-tlaft()¥l : O. DeDI'fou -tnu. ~ tut t»'la -flu.. (.esu.l~ is fosi-t1~, rC}tnt h6.V€ W~)?

lu- D: 11u.- WevrA- ~l,t ~.e.. ~'U.- illf1.l.V)

S :~ wW\%' +h-t tv>t 9L~;UtI is poSi.flve. . G~"fWLlid: P(DIS)= f(SID) prO) ~ P(Slt)- 0.05

P{S) foS',+i"~ tl/>T wl-thowt-ill~

= pes l D) Pe D) «().qcU(o .00012 - 0 ')- o· o~f[~ID)fCD)+ P(slli )f(pl} (O.ffq)(O.006J)+ (o.05){ 1- o.oot)-rcf ..h~YUA1 ~,l L5 J,l3 -1 ~, 146 R.l48 5epi 'a5" :)j)l~

:\\=~.ll5 ~ 9~ PN5LtU-eS5 ro-fe -ni. (Z7~~5~) 9.3'/. ( z~Cf/~o)~mAA. 5~n..e.. Cl?' /. (~,/ <61) iY/ (c34/z70)la,~ SP,ru, 13·j. (IQZj263) 6qj. (s5/~ J

P~vvaAlfttl 0.5) = ~!f' i:: + ~ , J10 = 0.18

f(ov~ ~ PW) = ~ ~-!fo+ ~~, JI~ := O· g3\ ~ StAtiFiJ SlACU--SS .fu:lllAf"e.. 5;~i<..

[~ S~ lOll. 9-1 263SYf\OJ I c-\oYl--<- 'if I 6 1/1

f(lr) z: 0.5 P(8) = 0.2.

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10 .>fudy Q pmba,hilily djstrib~/-fiuf7, we (){#,n /oak ar:(])Mean: M~I,(I'e of cuvter 0r J'I'7)dd le.@ Vafianr.e/50 ! Heasuv.e, ()f fJJe d'isp~7ot} ~ VIJ/ria.bihty tJ--tlu dgmhu-fin;;1 .'/

- J. _~I eoo flIlD/1 ~(- prOW'/'7~~; cuso Coiled .u:reCl~ V~iU- E riR-nukJ btJ .P- ~ ~71!al e:rAlrf,;J:jwfiDt7 X.# :::::EO<) = ~~ -+ prPbaiJ1litTj pllU$ fuY){-H,1/ -PtX) ~ f{K=?L)

~ :fat iaOlf . i.S de.ll0+e4 as (/2 or V(X):(/2.:: v (X) == E(x-}Lt" = ~(1<.-#)~;{X) = ~'X2.fOg_).L7

. ---P ~ Is duottJ b~ ()n-_ r::2 .v - .Jf.t-...--"~"'4IU~

. kX~ POr' qL(/c :;, it1 EN~~ 31'1 ~.s 5 qUMllot1S .• Result of ~/5 qut» -IoJJow0... O. P f): dfwf.fe ~~Iifl.1 ditfy;J,ufiPto 1UMfJOIJ 1J'I4.1ttJ torfuf.l'J :. ID ~

I I},fj

~ 403 65~ 305 to

11 I le n., bo 1- hl-u di5-fribufion:0/ Pro.VJ lA. 3to-fl1 "G('re!.-Ul"Tid "U'IV pro "-'C}I l'dtow 9f1.A~ : Jjt)

J,P: Pyplzal:iihhj HMs --&'ncfio Yl .

SUppD5-e X is a {;/iJU~ ra-nJorn va;rio.bk. w.H, .,n '/ f~S.5' bJc. vaJkU :X, ~ 'X2, ~ ~ = :» Xrt.

~ p>17bev(,)/,-A:J. Wl4~ ~nc-ti6vtf(~i) I l~i.~ n -=

ls ddine.£A ~ I-Pc Xi.):= p( X :::?l~)lPY()wt11.SCV !.-.p~)=: I@ .f(?l.i,) z 0

..Lx~~ 8Q;~ b~o1--~ ~~l D(~k.-P (0 h.tid) = f (IX,) -== f(X= x,) =it. +>(7<11)::= ..fl(x,) + f'(x~) + f'(~) t f(){q) /

== ..L -t 3.. -+ loT..L - I3~ 8 8 8 & -~{Urr1mVf.fa flve dlst{. b!c1tlo(Z £,1.(JC;ttoV1 (CD EL .

WF of 1Cit y?tttdaM I/a-ria,b/..e. is, awoftd by 1/ fex-) tt ~ is dd1vuJ by[f (~)=: f (X s. ~) ::: ~" ~~~) (

(0 F ha.s th« folloVJit1d propU+1-e5<D D< F('X-) 5 I® if ?f-s-I<J ~ F(~) .s F{:!)

~ ~i~ bCL~k -to f(bVious ex(j~F(~) = ..p{o ht.Nl) -t -f( I hu4J) + -P(J.huuk)

=- ~ + 1- + ~}tot. ce that f (I hu..J; ) ~ F ( {l ht".d})

\ z, 5 9/gtall Va(i 11:e ~ Y1 ~(./J( ii rr a..

_ .:z8

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{'i1.i«,1I l~::: 0 (I'IDtke4C-o((v-tly

x,.={1 If )

~::: l:t If 'J-f{'lt)OS

-:p 'f(?l.,) ~ t -:::0.056

~ f('4):: ~ = 0.13, I

-=* -ftot,) j O· VJ-

N J -j} f(~) = o·3hl1 ~ ~(t;{s).:= O,ibrt -7 ~(~) ~ 0-056

(

o ·/.3f +------tJJI

6.oS6-+-..IIIIIIL.~~~"""" ----I~ l£~I ~)(~ "X.lj >i, ~6

r"'HWb) Find m~n, VaYiana (MIld S.D .

EO<)= -;;;~.p(xj,)= [OlO.1756) + I(o.t« If) +2(O.V2)-t3(O.36J)+-4(f)·Jb7)+5(O,~6)J = ~? {JiJcrete Ufll-hyWl DiS,frihvt+joV1 (DUD)

IItr D. U.0 -then. ~~} P- Jirvlft-. Yl~ of p{)~i:fiv'L volwu ~ UJ.£i1 tLS - Ufwd fwbahiNy as ot:Ju.r...SD d tl1f?/lrt,.. (M"e.- ilyvll pO~~ible Out-UTlUS : X,; 'X..J..., =, Xn -6htrt -P( Xi) := i --floy J.s. i ~ '1

Meoa/ Valiance. Jf X i.s a. Ji.!.crbf~ rtLf1.tiot?? varJa}JI-!.- "n £lJr7Qcuf/Ve. itr1egers~ ('(+1, a ta , ..- "b ;« r: Eex) = b -r tL

~J ~2

0-2 = V (J() = ( b - 0. +-1) - I12

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Binomial R.V (tCa~ Vcpr~qjl~.) /i eJ1~·X" 1.5 tJu., ntt~ 6; SLUte;,5 JOY' "nil -truds (-tr\~s )

X~ BJN( n-, f)/ ) <., fYQ~~I;ty o~ .SUCC.eS.5

d~tt6 ~ 0 vciah

-f~ = xn i' ~p!.~~r.rIN"""" ?<.... 0.) I J . - - ~ fl-

~ r... will -loss a coin 5 iiY1Jt.J. Wfu.r is fJtv ~i/ifj -tJ.J L ~frd,ctltj 2, l/uuJs?

hJ succos bl, ¥#i.-, (L. hu.4X = J.. o/l.-~ 5 p::; Yz

-PC-X) = (~) (1 - fJ n-x f)t'-t~) = (~) ({)3. (+)~z: .5 C ~ (i)(t) : ~ ~[0, 3j.{5 I

~ .4 U»tfany ~Jucu ~vvkr ffA,'f"b r 2.,1. 4- al! ~w- pyooltAAi:J Ch"e.

dtf-.u-ave--. IF f(OU plc;k £0 ~ oA- Y()/}1.J.rnt-} whJ's pY()W;/ifr;;. IfOU %4leAll t. daect:W'e- pO/f-l (~ t'101r- -11LJD4mum.) ~'iI?'7I1M.

1M X be. t;Iu. 'YL{)~ 6f tkteclilk.- pDr4s_P(X>I) z: P(X=='l) f f{x~2) f --. + ro -= 10)f(~/) ~ J - P(X(I) =- J- f(x;{))

=9 1- (l~)(D.<18/° (0. o:l)0

-[0. 1831f7jy a b~ orniaL· tc

#x:: E=(X) ::: Y1·f2 x: V X =

CU.O(nl:tfi, R.. VIn, a. ~itJ of BJJtmoulh f::y201s

JIP- iJu. random VJ.11tWLe X cle.vrcJe ~

~ o? fA' ials W1til ..J:Ju. ~ rS t SU((eJ.5) ""fhut X is a. tjGO~-fri c Yl)I'7dom

v.."w,k. [p(-;()" (/- fp-i r] X= t,»: 3, .- -

Pat!11Zk. ~ pY17baJ"Ii/: fJru- (J.- LWtv C4Ylioit'U> CL. I~ (br6oU. sf. CIYt-&r-f'YI lY/o-flol1

is 0 .ol - If it I> OfJUWldfil.tif & IV~ Me jn~ u;htJt}- cS --tit..e.pwbwb7h~ i;hJ Ua.e-tl'l I~ wa-lz?r YJ..l4i. to be. an.oJytd ~ a. ~pal"tldt, U cJcI-euted?

X "V tiED ( P = 0-01.. X= 125)P(X=-I2SJ:: {t;·'11yZlf (0-01/ =- 0.0029

fo oriable

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