Guía - 3 - Ejercicios - Sobre - Variable - Aleatoria - Continua OK

July 26, 2022 | Author: Anonymous | Category: N/A
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     

Rcracgjm Cjmctkrac Rcracgjm cjmctkrac dkotaouc. Buodaôo nm ducotæc y buodaôo nm nmosancn. Rcjkr Mspmrcnk y Rcracozc nm uoc vcracgjm cjmctkrac. 

RCWACGJM DKO^AO]C 3.  Jc vmotc fmosucj nmj nmtmrhmotm ‚Gjcoquatc ‖, mo fajms nm skjms, nm uoc dcnmoc jkdcj nm tamoncs, ms uoc vcracgjm cjmctkrac, U, qum sm pumnm pumnm fknmjcr dko uoc buodaôo nm nmosancn nmosancn nm  prkgcgajancn (b.n.p.) nm jc bkrfc sahuamotm9 sahuamotm9 W9 4/8 

   

,

3: x ≮ 7 

c)  Ecjjcr mj vcjkr nm jc dkostcotm l.

U9 Rmotc fmosucj nmj nmtmrhmotm Gjcoquatc (mo fajms nm skjms).   Wx6 3:

x ≮ 7 

∬∗  3. ∬    3

b(x) ms uoc buodaôo nm nmosancn nmosancn nm prkgcgajancn, prkgcgajancn, motkodms motkodms sm dufpjm qum9

 

 

 

      6 9    3↗ 4    

Mo mstm dcsk tmomfks9

 

Wmskjvmfks jc aotmhrcj y nmspmicfks

 

 

6

8  ↗  4    ↗   

Cekrc scgmfks qum L64/8, motkodms9

3

 

 

  /

,

3: x ≮ 7 

 g)  Nmtmrfaom mj vcjkr vcjkr mspmrcnk y mj dkmbadamotm nm vcracdaôo vcracdaôo nm jc vmotc fmosucj nmj nmtmrhmotm ‚Gjcoquatc‖.

Jc mspmrcozc nm U 6 vcjkr mspmrcnk nm U 6 prkfmnak pkgjcdakocj nm U 6 fmnac pkgjcdakocj nm U, mstã ncnc pkr9 M( U)



 x b ( x ) nx WU

6     4 4           8  8  > 6  .. .    

 pkrqum ms uo nctk qum sm rmquamrm pcrc

^cfgaáo ecjjcfks jc ecjjcr jc R(U)9 

M( U 7 )





x 7 b ( x ) nx

WU

 

          6   48  48 = 6  .. .

 

Jc vcracozc ms9

      

 

Wmmfpjczconk jks vcjkrms9

  7.2=833.2083 

Jc Nmsvacdaôo mstãoncr ms9

τ   RRxx

 

7

0.08>471=1

 

   

 

τ  ∙ 0.0.08>4

 6 0.78724>=> 

Mj Dkmbadamotm nm vcracdaôo nm jc vcracgjm U, mstã ncnk pkr9

    ∘300        

 

Nkonm9

 

0. 7 8724>=>   .     ∘300 ..   3232..12 % 3.2083

 

 . Mj DR ms fmokr c 40%, motkodms sm kgsmrvc ekfkhmomancn mo jc nastragudaôo nm jc vcracgjm U. U. W9 M(U)6 M(U)6 3.2083< M(U7)67.2=83< R(U)60.08>4< DR(U)632.12 %

Cnadakocj 39 ^momfks jc vcracgjm Q nmbaoanc nm jc sahuamotm fcomrc9 Q 6 =U + 4.7= Ecjjcr mj DR nm c vcracgjm Q »Mo jc nastragudaôo nm duãj nm jcs vcracgjms (U k Q) sm kgsmrvc fcykr ekfkhmomancn;



y 6 M(Q) 6 M(=U + 4.7=) 6 =*M(U) + M(4.7=) 6 =* 7

3.2083

 + 4.7= 6 33.75==

 6 R(Q)6R(=U+4.7=) 6 7=*R(U) + R(4.7=) 6 7=*0.08>471=1 + 0 6 3.5=57418=

Cekrc ecjjcfks jc nmsvacdaôo mstãoncr nm jc vcracgjm Q qum qu m ms jc rcæz nm jc vcracozc9

τyτy  RyRy ∙ .. MQ ∘300  6

DR(Q) 6

 6 3.424387285 

3.424387285/ 33.75==*300 6 37.08518>2 %

4

 

»Mo jc nastragudaôo nm duãj nm jcs vcracgjms (U k Q) sm kgsmrvc fcykr ekfkhmomancn; 

.    3232..1212 % .  :.  , ..ô ℏ  3737..05%ℏ    

 

 

Cnadakocj 79 U9 Rmotc fmosucj nmj nmtmrhmotm Gjcoquatc (mo fajms nm skjms).  Wx6 3:



x ≮ 7 

,

3: x ≮ 7 

  /

Tm scgm qum jcs vmotcs nmj nmtmrhmotm Gjcoquatc sko mxdmjmotms duconk sko fcykrms c 3=00 skjms. Dcjdujm jc prkgcgajancn qum jcs vmotcs nm n m nmtmrhmotm Gjcoquatc smco mxdmjmotms. Kgsmrvcdaôo9 3=00 Tkjms 6 3.= fajms nm skjms (dkosanmrconk jcs uoancnms nm jc vcracgjm nm mstunak) P(vmotcs nm nmtmrhmotm Gjcoquatc smco mxdmjmotms) 6 P( U ? 3.=) P( U ? 3.=) 6

 4 0.22083>75=8 . 8

 

>

7. 

PP^ R. CJMC^KWAC DKO^AO]C 9 MIMFPJK 3 9 Mj tamfpk U, mo ekrcs, qum sm aovamrtm mo moscfgjcr damrtk crtædujk sm pumnm fkn fknmjcr mjcr dko uoc buodaôo nm nmosancn nm prkgcgajancn (

b.n.p.) nm jc bkrfc sahuamotm9

 

  b  x    0 x >  lx 0 ktrk kt rk dcsk dcsk  c)  Ecjjcr mj vcjkr nm jc dkostcotm l.

W93/5 

U9 ^amfpk qum sm aovamrtm mo moscfgjcr damrtk crtædujk (mo ekrcs).  

\0V…Wcohk k rmdkrrank (dkoiuotk aobaoatk nm vcjkrms)  Wx6 \0V… nmosancn nm prkgcgajancn, prkgcgajancn, motkodms sm dufpjm qum9 b(x) ms uoc buodaôo nm nmosancn

     

    7 >      50  ↗    ↗7 05 50   

 

 

 

…….3/5 =

 

 

 g)  Dcjdujcr jc prkgcgajancn nm qum mj tamfpk nm moscfgjcim mstá motrm 3.= y 4 ekrcs. W90.>7358=   Cekrc rmmfpjczk L63/5 mo b(x)

b(x) 6

U nkonm9 0:6 x :6> 

3/5

U9 ^amfpk qum sm aovamrtm mo moscfgjcr damrtk crtædujk (mo ekrcs).  

Wx6 \0V 

.::    6 .  6.   35 1735 3 7.77=3570.>7358=

 

d)  Ncnk qum (Ta) mj tamfpk nm moscfgjcim nm damrtk crtædujk ms pkr jk fmoks uoc ekrc y fmnac , »Duãj ms jc prkgcgajancn nm qum jc nurcdaôo nm mstm moscfgjcim smc nm c jk fãs 4 ekrcs; W9 0.>10101 

Prkgcgajancn dkonadakocj9 Prkgcgajancn nm jc aotmrsmddaôo motrm prkgcgajancn nm jc dkonadaôo.  

  ≮  /  ≭3 .   . ≭≮≮ .   ∬ . 5   0.>7358= 0.>1013 .∬  35  0.5=148=

 

2

Nkonm9  

 3 3  6 3 32 7.7= .   6. 6.   0.5=51478=  5  7  7    5   

4.  PP^ R. CJMC^KWAC DKO^AO]C9 MIMFPJK 79 Mj pkrdmotcim nm utajancn mo uoc trcoscddaôo mdkoôfadc mdkoôfadc ms uoc vcracgjm cjmctkrac duyc buodaôo nm nmosancn nm prkgcgaja prkgcgajancn ncn

(b.n.p.) ms jc sahuamotm9 0     x   3  

b(x) 6 l x7

aobaoatks vcjkrms. vcjkrms. Wx 6 Motrm 0 y 3 ecy aobaoatks

Wx6 \0027= 

 

d)  Ta (ncnk qum) sm scgm qum mj pkrdmotcim nm utajancn ms supmrakr c 8=% »Duãj ms jc prkgcgajancn nm qum smc c jk fãs 10%; W9 0.=437>4 

Wmdkrnconk9  ]oc prkgcgajancn dkonadakocj sm rmsumjvm csæ9 mo mj oufmrcnkr9 jc  prkgcgajancn nm jc aotmrsmddaôo y mo mj nmokfaocnkr9jc prkgcgajancn nm jc dkonadaôo.

  ≮ 0.10 ∬/. 4?.0.40837= 0.?. 8=:≮0.10  ∬.. 4  0.=8537= .

 

n)  Nmtmrfaom mj vcjkr mspmrcnk, jc vcracozc, jc nmsvacdaôo mstãoncr y mj DR nmj pkrdmotcim nm utajancn nm nadec trcoscddaôo mdkoôfadc (U). W9 M(U)6 0.8=, M(U7)60.20, R(U)6 0.048=, x60.3142>1, DR(U)67=.57% 

b(x) 6

    

 9 0      x   3  

Wx6 \0 3    0   4  4/>3  0

0.8=

0 >

 

M(U) 6  6 0.8=

M( U

(Rcjkr mspmrcnk 6 Fmnac k prkfmnak  pkgjcdakocj)    pkgjcdakocj)

7

)



7

x b ( x )nx

      3  =        0.200      0.200.8= 0.048= WU

 

 4/= 3   0 4 =      

0.200.=27=0.048= 30

 

 

 

 

Nmsvacdaôo mstãoncr nm jc vcracgjm U9

τxτx  RxRx

 

  ∙ 0.0.0 48=0. 3 142>1     ∘300

   

0. 3 142>1   .     0.8=  ∘300 ∘300..   %

 

Mj DR ms fmokr c 40%< motkodms sm kgsmrvc ekfkhmomancn mo jc nastragudaôo nm jc vcracgjm U.

m)  Tupkohcfks qum nmgank c damrtcs fmnancs nmdrmtcncs pkr mj hkgamrok, mo jcs trcoscddakoms mdkoôfadcs nmj mimfpjk nmscrrkjjcnk cotmrakrfmotm mj pkrdmotcim nm utajancn kgtmoank sm ec fknabadcnk nm jc sahuamotm sahuamotm fcomrc9 Nkonm

Q 6 3.=U + 0.8 

Q6 Oumvk pkrdmotcim nm utajancn nmspuás nm jcs fmnancs nmdrmtcncs pkr

mj hkgamrok (nmspuás nm rmcjazcnc jc fknabadcdaôo).  Nmtmrfaom jc fmnac, jc vcracozc y mj DR nm jc utajancn utajancn jumhk nm rmcjazcnc jc fknabadcdaôo. fknabadcdaôo. DR(Q)63=.13%   W9 M(Q)63.57=, R(Q)6 0.05>48= DR(Q)63=.13%

3.=0.8==+0. 8...+. +.   3.3.==  +0+0. 8 

……..Rcjkr mspmrcnk k fmnac pkgjcdakocj pkgjcdakocj

nm jc vcracgjm Q 

7.7=∙ 0.0∘.00.5>48= 048=  .    

Nmsvacdaôo mstãoncr nm jc vcracgjm Q9



 

0.710>848= 

 

..   ∘300  ∘300 0.710>848= 3.57=  ∘ 300  3=.132> % 33

Mj DR(Q) : 40% Motkodms sm kgsmrvc ekfkhmomancn mo jc nastragudaôo nm jc vcracgjm Q.

Cnadakocj9

»Suá nastragudaôo ms fãs ekfkháomc, jc nastragudaôo nm U k jc nastragudaôo nm Q;  

DR(U) 6 DR(Q) 6

 

3=.7=.1532>311%%

  Jc nastragudaôo nm jc vcracgjm Q ms fãs ekfkháomc 9 DR(Q) : DR(U) >.  PP^ R. CJMC^KWAC DKO^AO]C9 MIMFPJK 4 9 Mj tamfpk U, mo ekrcs, qum sm aovamrtm mo moscfgjcr damrtk crtædujk sm pumnm fknmjcr dko uoc buodaôo nm nmosancn nm  prkgcgajancn (b.n.p.) nm jc bkrfc sahuamotm9 sahuamotm9

0:x:3

b(x) 6 7x,

Wx 6 0 —  39  39 Motm 0 y 3 ecy aobaoatks

Dcjdujm jcs sahuamotms prkgcgajancnms9

vcjkrms aotmrfmnaks.

U9 ^amfpk qum sm aovamrtm mo moscfgjcr damrtk crtædujk (mo ekrcs).   Cnadakocj9 Ecjjcr jc Buodaôo nm Nastragudaôo Cdufujcnc B(U)9 Jc Buodaôo nm nastragudaôo cdufujcnc pmrfatm ecjjcr jc prkgcgajancn cdufujcnc c jc azquamrnc pcrc ducjquamr vcjkr nm jc vcracgjm U. »Dôfk; tcgujconk mj vcjkr nm jc vcracgjm mo B(U).

Jc Buodaôo nm nastragudaôo cdufujcnc9 B(U )

sm nmoktc dko B

∬∗     ∟9        48= 

Mo mstc prmhuotc prmhuotc sm panaô ecjjcr9 Jc prkgcgajancn prkgcgajancn nm qum sm aov aovamrtc amrtc fãs nm >= faoutks mo jc jc rmpcrcdaôo nm nadek crtædujk.

(  ? >= )   ? 0.8=8= ℏℏ

Wmdkrncr qum jc vcracgjm nm mstunak mstã mo EKWCT.  

>= faoutks 6 ¿ ekrc 6 0.8= ekrcs

3>

 

AFPKW^CO^M 9 JC prkgcgajancn nmgm pjcotmcrsm dkosanmrconk jcs fasfcs uoancnms nm fmnanc nm jc vcracgjm nm mstunak.

Ktrc bkrfc nm nmscrrkjjcr mstm mimrdadak smræc9

  ? 0.8==  . 7 777 76.6   0.>48=

 

Tao mfpjmcr jc B(U)< ecgamonk aotmhrcnk mo dcnc dcn c trcgcicfks csæ9

c)  Ecjjcr jc prkgcgajancn nm qum mj tamfpk nm moscfgjcim nurm c jk sufk 40 faoutks (fmnac ekrc). W90.7= 

U9 ^amfpk qum sm aovamrtm mo moscfgjcr damrtk crtædujk (mo ekrcs).   Dkfk jc vcracgjm vcracgjm mstã nmbaoanc mo ekrcs9 40 faoutks 6 fmnac ekrc. Fmnac ekrc sm rmprmsmotc pkr 0.=.

6.  .      ≮ 0.=   7 777  7 6 0.7=

 

60.= ekrcs ms mj vcjkr nm jc vcracgjm U qum nmic c su azquamrnc jc  prkgcgajancn nm 0.7=< 0.7=< ms nmdar mj 7=% nm jks nctks< motkodms motkodms 0.= ekrcs ms mj Pmrdmotaj 7= k Ducrtaj 3 (ms mj vcjkr fãxafk nmj 7=% aobmrakr pmrk tcfgaáo ms mj vcjkr fæoafk nmj 8=% supmrakr).  g)  Ecjjcr jc prkgcgajancn nm qum mj tamfpk nm moscfgjcim nurm dkfk fæoafk fmnac ekrc.

W9 0.8= 

Dkfk jc vcracgjm mstã fmnanc mo ekrcs, fmnac ekrc sm rmprmsmotc pkr 0.=.

6      ≭ 0.=  . 7 777  7 6. 0.8=

 

Ktrc bkrfc9

  ≭ 0.= 3  : 0.=  3=

 3 —   3  —  0.7=  0.7= 6 0.8= 

 

d)  Ecjjcr jc prkgcgajancn nm qum mj tamfpk nm moscfgjcim nurm fãs nm uo ducrtk nm ekrc  pmrk fmoks nm trms ducrtks nm ekrc (fãs nm 3= faoutks pmrk fmoks nm >= faoutks). faoutks) . W9 0.=0 

U9 ^amfpk qum sm aovamrtm mo moscfgjcr damrtk crtædujk (mo ekrcs).   Dkfk jc vcracgjm mstã nmbaoanc mo ekrcs, uo ducrtk nm ekrc sm rmprmsmotc pkr 0.7= y trms ducrtks nm ekrc sm rmprmsmotc pkr p kr 0.8=.

6.   .     0. 7 =::0. 8 =  . 7 777  7 6. 0.=

 

n)  Ecjjcr jc prkgcgajancn prkgcgajancn nm qum sm aovamrtc aovamrtc fãs nm >= faoutks mo moscfgjcr moscfgjcr nadek crtædujk. W9 0.>48= 

U9 ^amfpk qum sm aovamrtm mo moscfgjcr damrtk crtædujk (mo ekrcs).   Dkfk jc vcracgjm mstã nmbaoanc mo ekrcs, >= faoutks rmprmsmotc 0.8= ekrcs.

 0.8= 6      ? 0.8=  . 7 777  7 6. 0.>48=

Dkovmrtar >= faoutks mo ekrcs9

 

 

=.  Mo uo dmotrk dkfmrdacj jcs vmotcs nacracs (mo fajms nm skjms)  ms  uoc  vcracgjm cjmctkrac U, dko dko buodaôo nm nmosancn nm prkgcgajancn9

   ≮:        ≮: 0 ktrk dcsk

 

Tm tamom jc sahuamotm aobkrfcdaôo9

  Ta jcs vmotcs nacracs sko c jk fãs 7.7 faj skjms skjms, sko jjcfcncs vmotcs



32

gcics. 

 

  Ta jcs vmotcs nacracs nacracs sko fcykrms c 7.7 faj skjms pmrk ok



fcykrms c >.= faj skjms sko jjcfcncs vmotcs rmhujcrms.    Ta jcs vmotcs nacracs sko fcykrms c >.= faj skjms  sko jjcfcncs vmotcs



cjtcs.

c)  Nmtmrfaom jc prkgcgajancn nm qum mj dmotrk dkfmrdacj tmohc vmotcs rmhujcrms. W9 0.50=5

U9 Rmotcs nacracs nacracs nm uo dmotrk dkfmrdacj dkfmrdacj (mo fajms nm skjms) 

       ≮   ≮   

 

 

   

 

   ++ .     0.50=5

 7. 7 :≮>. =  . 

0.22

 

+ 0.3>=54444 6

 

0.50=5

 g)  Nmtmrfaom mj dkmbadamotm nm vcracdaôo vcracdaôo nm jcs vmotcs nacracs nmj dmotrk dkfmrdacj. W9 M(U)64.8885< M(U7)63>.5551< R(U) 6 0.2384< DR(U)6 70.8184%. 70.8184%.

M( U)





x b ( x ) nx

> 2 7      ∬7   4  ++ ∬>    4.8885 WU

 

 

(vcjkr mspmrcnk9 fmnac k prkfmnak pkgjcdakocj)

7.7777 M( U

7

)

+



3.====== 6

4.8885

7

x b ( x ) nx

WU

 

    7          4  ++      3>.5551

 

8.===

+

38

8.4444 6

3>.5551 

 

 

            RRxx 0.2384        NmNmsv(sva acdada)∙ ôoô0.0o.2mstmst384 .ããonconcr r nmnm UU.τ   

 

 



0.85=25>>7  

    ∘300

0.85=25>>7

.    

 

 

∘30070.818%

.

DR (U) : 40%, sm kgsmrvc ekfkhmomancn mo jc nastragudaôo nm jc vcracgjm U.  

35

 

PWKGJMFCT NARMWTKT9 ^CWMC 34. PP^ PP^ R. CJMC^KWAC DKO^AO]C (MIMFPJK > NMJ PP^)  Jc dcotancn rmcj nm dcbá (mo hrcfks) mo uo rmdapamotm nm 740 hrcfks jjmocnk pkr damrtc fãquaoc ms uoc vcracgjm cjmctkrac duyc buodaôo nm nmosancn nm prkgcgajancn mstã ncnc  pkr9 b(x)6 3/=

778.=  x

  747.=

c)  Dcjdujcr jc prkgcgajancn nm qum uo rmdapamotm nm 740 hrcfks dkotmohc ducotk fudek 775.2= hrcfks. W9 0.74 

 9

 dcotancn rmcj nm dcbá mo uo  dcotancn u o rmdapamotm nm 740 (mo hrcfks).  hrcfks). 

.   ≮ 775.2==  . 3= 0.74

 

 g)  Dcjdujcr jc prkgcgajancn nm qum uo rmdapamotm dkotmohc motrm 775.2= hrcfks y 747 hrcfks.

W90.28 

 3 775.2=::747  . = 0.28

 

d)  Dcjdujcr mj dkotmoank mspmrcnk nmj rmdapamotm. M(U)9 740 

.      .  3=  740

 

n)  Dcjdujcr jc vcracozc nmj dkotmoank nmj rmdapamotm y mj DR.

W9 M(U7)6 =7,107.0544 =7,107.0544 , R(U)67.0544, x63.>>4, DR(U)6 0.278% 

   ..  3=  =7107.0544

 

31

 

          7.0544 ..   ∙ 7.7740.0544 ∘3000.278 %  

Wmmfpjczconk kgtmomfks

 

Ecjjconk mj dkmbadamotm nm vcracdaôo tmomfks

 

38. PP^ PP^ R. CJMC^KWAC DKO^AO]C (MIMFPJK = NMJ PP^)  Jks aohrmsks nacraks qum tamomo jcs tamoncs qum dkfmrdacjazco ùtajms msdkjcrms y nm kbadaoc mo jcs hcjmræcs nm uo dmotrk dkfmrdacj sko uoc vcracgjm cjmctkrac, mxprmscn mxprmscncc mo fajms nm skjms, duyc buodaôo nm nmosancn ms jc sahuamotm9 4

b(x) 6

4  x 

7

   

7

 x 

>

 

0:x:7

c)  Ecjjcr jc Buodaôo nm Nastragudaôo9 B(x) nm U.

 9

aaohrmsks ohrmsks nacraks qum tamomo jcs tamoncs qum dkfmrdacjazco ùtajms msdkjcrms y nm kbadaoc mo jcs hcjmræcs nm uo dmotrk dkfmrdacj (mo fajms nm skjms).

         ::

 

 g)  Ecjjcr jc prkgcgajancn nm qum mo uo næc jcs tamoncs tmohco aohrmsks supmrakrms c 3000 skjms. W90.=0 

 9

aaohrmsks ohrmsks nacraks qum tamomo jcs tamoncs qum dkfmrdacjazco ùtajms msdkjcrms y nm kbadaoc mo jcs hcjmræcs nm uo dmotrk dkfmrdacj.

   ? 3   47   4>  0. =

 

d)  Ta mj aohrmsk nm uoc nm jcs tamoncs mo uo næc ms supmrakr c 100 skjms, »duãj ms jc prkgcgajancn nm qum ok skgrmpcsm jks 3=00 skjms; W9 0.84 aohrmsks nacraks qum tamomo jcs tamoncs qum dkfmrdacjazco ùtajms msdkjcrms y nm kbadaoc mo jcs hcjmræcs nm uo dmotrk dkfmrdacj.

 9

70

 

. 47   4>   0.>35= ∬ 0. 1 ::3. =  .  :3.= / ?0.1  ?0.1  ∬. 47   4>    0.=8>8= 0.8753  

3=.  ]oc mfprmsc ec dcjdujcnk qum jcs vmotcs (R) y jks dkstks uoatcraks (D) mstão rmjcdakocnks dko mj æonadm nm prmdaks cj dkosufankr ( U ) fmnacotm jcs sahuamotms mducdakoms9

D  

3 ( x  7)   4

R  

3 (31   x )   4

U9 æonadm nm prmdaks cj dkosufankr ms uoc v. c. dko buodaôo nm nmosancn nm prkgcgajancn9

 b  ( x ) 

7   x  3  x  30   11

c)  »Duãj ms jc prkgcgajancn nm qum jc utajancn smc omhctavc; W9 ]6]tajancn6 (38 —   7U)/4 , Prkgcgajancn60.7504

]tajancn (])6 Rmotcs —  Dkstks  Dkstks 

31   7     4 444 ↗      38 7  :     4  4  : 0    ? 5.=  . 117    

 

0.7504

 g)  Ecjjcr jc utajancn mspmrcnc. W9 M(U)62.84, M(])63.35.

Ecjjconk mj prmdak mspmrcnk

 7 8>        2.8784 

11 33 73

 

 

    384  74    38  7   384 3.4 743∘45352.8784

 

 

 

 

 

33. Mj tamfpk nm nurcdaôo (mo cóks) nm uo nmtmrfaocnk dkfpkomotm nm uo iuhumtm mjmdtrôoadk ms uoc vcracgjm cjmctkrac qum tamom pkr buodaôo nm nmosancn9

7 x sa  0   x  3

b(x)  

0

ktrk dcsk

c) Ta sm mjahm uo dkfpkomotm »Duãj ms jc prkgcgajancn nm qum nurm fãs nm > fmsms; f msms; W9 0.5555551

   \ fmsms mo cóks kgtmoamonk

, safpjabadconk jc mxprmsaôo .

 

 g)  »Duãj ms jc nurcdaôo fæoafc nmj 30% nm dkfpkomotms dkosanmrcnks jks nm fcykr nurcdaôo; W9 L60.1>58 cóks

 

9 tamfpk nm nurcdaôo nm uo nmtmrfaocnk dkfpkomotm nm uo iuhumtm mjmdtrôoadk.



Dkosanmrconk  jc nurcdaôo fæoafc nmj 30% nm dkfpkomotms dkosanmrcnks nm jks nm fcykr nurcdaôo. L ms mj P10 (ms mj vcjkr fãxafk nmj 10% 1 0% aobmrakr y ms tcfgaáo mj vcjkr fæoafk nmj 30% supmrakr)

77

  ≭  0.30  70.30

 

 

 

Wmskjvamonk jc aotmhrcj tmomfks

3\ V6660.300. ↗ 1030  0.1>58

7/7 Nmspmicfks L 9

 

 

Jc nurcdaôo fæoafc ms 0.1>58 cóks. Ktrc bkrfc9

 

  ≮ 70.  3  0.310  0.10  

Wmskjvamonk jc aotmhrcj y nmspmiconk L6P106 0.1>58 cóks 

d)  Tupkohc qum mj prmdak (Q) nm mstks dkfpkomotms mstã rmjcdakocnk dko mj tamfpk nm nurcdaôo nm jks fasfks, nm fcomrc qum9 Q 6 0.5U +3 »Ms jc nastragudaôo nmj prmdak nm mstks dkfpkomotms (Q), fãs ekfkháomc qum jc nastragudaôo nmj tamfpk nm nurcdaôo nm jks fasfks f asfks (U); W9 DR(U)6 4=.4=% , DR(Q) 6 37.718% , DR(Q): DR(U)  

Pcrc cocjazcr jc ekfkhmomancn sm dcjdujc mj dkmbadamotm nm vcracdaôo nm jcs vcracgjms m  y jumhk dkfpcrcrjks.



 

Cocjazconk jc vcracgjm

 

 

 

9 tamfpk nm nurcdaôo nm uo nmtmrfaocnk dkfpkomotm nm uo iuhumtm mjmdtrôoadk (mo cóks).  cóks). 

     7 74        7 3       ( )  37 774  3535  

 

 

74

 

 

3   ..   7435 ∘ 300  4=.4==4 %

 

  .  + 0.5  +30. 5 +3         .  +  0.5   +00.5 +0  5   ..  743=77= ∘ 300  37.718= % Cocjazconk jc vcracgjm   Q 6 0.5U +3 

9 prmdak nmj dkfpkomotm nm uo iuhumtm mjmdtrôoadk.

 

 

 

Dkfpcrconk mj dkmbadamotm nm vcracdaôo nm jcs vcracgjms

.. :.

 

Jc nastragudaôo nm jks prmdaks nm dkfpkomotms (Q) ms fãs ekfkháomc qum jc nastragudaôo nmj tamfpk nm nurcdaôo nm dkfpkomotms d kfpkomotms (U).

7>

 

Mimfpjks nm dôfk aotmhrcr9

 6 .∬.7  6. 6.   6  77 7 7 7\V7 7 6.   7 33 0.8=  7(3-0.=) 6 3 

0. > 48= 

 

 6  4 4 4 6 4/4 4/4  3  0   4 4 6  

 

. 4/> 6.   6  4/>  3  > 0. =  0. 8 0437=  . 4 4  = 6.   

4/=3  0.=  0.=537= 4/= 7=

 

72

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