BENAVIDES

 

IASWABB BCWWA[N MALE_CKAW [ABBAY ALOA]FA]CE CC EÕJ []EMEIJ MCJAW[EKCW[CGE   AIA]GCGCJW P]JPQAW[JW 5.

Qle gjfpeõæe fel feluoegturare uoegturare utcbcze ul a asquafe squafe pere be

egaptegc÷l ka bjs ertægubjs prjkugckjs eltas kapere sar afmergekjs. Ab pbel as ka kjs atepes. Wa praperel geies ka =1 afmerqua y sa sabaggcjle ule fuastre ka 7 pere varcocger sc tcalal ebhùl ertægubj kaoagtujsj. Wc sa algualtre ulj, be geie altare sa rahrase pere varcocgerbe eb 500%. Wc lj sa algualtre lclhùl ertægubj kaoagtujsj, be geie sa afmerge. e) ºGuåb as be prjmemcbckek ka qua sa afmerqua ule geie qua tcala tras ertægubjs kaoagtujsjs:, m) =. ºGuåb as be prjmemcbckek ka qua ule geie qua gjltcala sjbj ul ertægubj kaoagtujsj sa rahrase pere varcocgegc÷l:

7. Ql fezj fezj ka mereie mereie aspeõjbe aspeõjbe tala tala ;0 geres geres,, ka bes guebas guebas 50 50 talal talal jrj y bes bes raselas 70 lj bj talal. Wupjlhefjs qua ka asa fezj sa axreal eb ezer 8 geres, bes guebas lj sa raclgjrpjrel eb fezj.

 

Wc ^ as ab lùfarj ka jrjs prasaltas al bes 8 gertes axtreækes, altjlgas be prjmemcbckek qua sa talhel x jrjs al ule axtreggc÷l ka 8 gertes astå kekj pjr be kcstrcmugc÷l ncparhajfãtrcge ncparhajfãtrcge P(;0,50,84x). _aefjs astj esæ9 pere gebguber be prjmemcbckek ka talar ; jrjs al ule axtreggc÷l ka 8 gertes usefjs be o÷rfube ka be kcstrcmugc÷l ncparhajfãtrcge ncparhajfã trcge gjl bjs schucaltas vebjras9

 S ab rasubtekj as9 ;,18% ka prjmemcbckek. prjmemcbckek. Parj sc sa qucara semar be prjmemcbckek ka jmtalar fås ka ; gertes, altjlgas nemrå qua sufer9 P(;)+P(1)+P(?)+P(8)61,=0% 

7. Qle oåmrcge ka prjocbågtcgjs ne algjltrekj qua ka geke 5000 prasarvetcvjs prjkugckjs pjr gcarte fåqucle, 1 sebal kaoagtujsjs. Pere aoagtuer ab gjltrjb ka gebckek sa tjfel eb ezer 500 gjlkjlas y ab bjta sa ragneze sc ney pjr bj faljs ulj j fås kaoagtujsj. ]aspjlkar9 e) ºUuã pjscmcbckek ney qua ul bjta ka 500 sae kasgertekj: m) ºAs aocgcalta asta grctarcj ka gjltrjb ka gebckek:

Al asta gesj vel e eperagar lùfarjs gjfmcletjrcj gjfmcletjrcjs s fuy hrelkas. Ab gåbgubj sa kcocgubte, e faljs qua sa kcspjlhe ka ul pequata clojrfåtcgj ekaguekj. Parj kamckj e qua sa trete ka ule pjmbegc÷l hrelka y be fuastre as kcaz vagas faljr qua be pjmbegc÷l tjteb, sa puaka negar usj ka be eprjxcfegc÷l ka be kcstrcmugc÷l ncparhajfãtrcge pjr be kcstrcmugc÷l mcljfceb9

 

P(5000,1,5004x) 6 Mc(500, 1/5000,x) 6 Mc(500, 0.001,x) 6 G(500,x)*0.001\x (50.001)\(500-x) 

Al be axprasc÷l eltarcjr G(500,x) as ul lùfarj gjfmcletjrcj. gjfmcletjrcj. Altjlgas be prjmemcbckek ka neye fås ka ulj kaoagtujsj sa gebguberå esæ9 P(x .?01> 6 0. 0.73;=  73;=  

Wa trete ka ule axgabalta eprjxcfegc÷l, sc sa ba gjfpere gjl ab vebjr jmtalckj eb epbcger be kcstrcmugc÷l ncparhajfãtrcg ncparhajfãtrcge9 e9 0.;50= Wa puaka kagcr qua, gjl prjmemcbckek kab ;0% ul bjta ka 500 prjocbågtcgjs kamarå sar kasgertekj, bj gueb rasubte pjgj aocgcalta. Parj, scalkj ul pjgj faljs axchalta al ab prjgasj ka gjltrjb ka gebckek y kasagnårefjs ab bjta ka 500 sjbefalta sc ney kjs j fås kaoagtujsjs, altjlgas be prjmemcbckek ka kasgerter ab bjta gearæe e epales >%.

;. Qle fåqucle ka egjs pbåstgjs oulgcjle ka eb ojrfe qua ka geke 50 pcazes, ule seba kaojrfeke. Al ule fuasre ka 1 pcazes qua pjscmcbckek ney qua ule sjbe pcaze sebhe kaoagujse.  

Pjmbegc÷l9 L650 Lùfarj l ka kaoagtujses pjr geke L9 l65 [efeõj ka be fuastre9 f61

P(50, 5, 14 5) 6 G(5,5)*G G(5,5)*G(3,;)/G(50,1)6 (3,;)/G(50,1)6 5*5=?/=1= 6 0.1  

Pjr bj teltj ney ul 10% ka prjmemcbckek ka qua al ule fuastre ka 1, ul tegj sebhe kaojrfa

 

  1. Al ule raulc÷l ka i÷valas megncbbaras ney 8 kefes y ? gemebbarjs. Altra bes gncges, ; astukcel nufelckekas y 7 gcalgces. Al ab hrupj ka gncgjs, 5 astukce nufelckekas y 1 gcalgces. Gebguber bj schucalta9 Abchcalkj eb ezer tras gncges9 ºquã prjmemcbckek ney qua tjkes e) astukcal nufelckekas:. Wc sa asgjhal eb ezer tras escstaltas e be raulc÷l ka efchjs9 ºUuã m) pjscmcbckek ney qua tras ka abbjs, scl cfpjrter saxj, astukcal gcalgces bjs tras, j nufelckekas tefmcãl bjs tras:. Wjbugc÷l e

Be pjmbegc÷l as ab lùfarj tjteb ka gncges9 L68. Bes qua astukcel nufelckekas nufelckek as sjl l6;, kab ttjteb. jteb. Be fuastre eb ezer ka gncges sarå ka f67. Al asa gesj be prjmemcbckek qua bes tras sael gurseltas ka nufelckekas astå keke pjr be oulgc÷l ncparhajfãtrcge9 P(L68, l6;, f67, x67) 6 G(;, 7) G(7, 0) / G(8, 7) 6 0.55;7 Altjlgas ney 55.;% ka prjmemcbckek qua tras t ras gncges abahckes eb ezer astukcal nufelckekas. Wjbugc÷l m

Bjs vebjras e utcbczer enjre sjl9 -Pjmbegc÷l9 L65; -Geltckek qua astukce batres as9 l6? y be -[efeõj ka be fuastre9 f67. -Lùfarj ka efchjs qua astukcel nufelckekas9 x Ka eguarkj e astj, x67 schlcocge qua bjs tras astukcel nufelckekas, nufelckekas, parj x60 schlcocge qua lclhulj astukce nufelckekas nufelckekas.. Be prjmemcbckek qua bjs tras astukcal bj fcsfj vcala keke pjr be sufe9 P(5;, ?, 7, x60) + P(5;, ?, 7, x67) 6 0.01?0 + 0.5173 6 0.=033

 

Buahj, talafjs ul =5% ka prjmemcbckek qua tras escstaltas e be raulc÷l, abahckjs eb ezer, astukcal bj fcsfj.

?. Axcstal kjs vegeltas al ab Kapertefaltj Astekæstcge ka pjstubeltas9 gcarte prastchcjse ulcvarsckek. E ul bbefekj e gjlgursj saka prasaltel gclgj tras tcalal axparcalgce al fjkabjs bclaebas y kjs al prjmemcbckek epbcgeke. Ab gjfctã ka mùsquake sa algerhe ka abahcr tras fcafmrjs al ojrfe ebaetjrce. ºGuåb as be prjmemcbckek ka qua kjs talhel axparcalgce al fjkabjs e. bclaebas: ºGuåb as be prjmemcbckek ka qua e bj fås kjs talhel axparcalgce al m. fjkabjs bclaebas: ºGuåb as ab vebjr asparekj ka pjstubeltas, al be fuastre, qua tcalal g. axparcalgce al fjkabjs bclaebas: Asquafe ka sjbugc÷l9  Pesj 5.  Ckaltcocger ab axparcfaltj9 Asukcer ab lùfarj ka pjsubelas qua talal axparcalgce al fjkabjs bclaebas 7 qua sa abchal ebaejrcefala ka alra bjs qua sa prasalel e ul bbefekj e gjlgursj.

Pesj =. Ckaltcocger ab tefeõj kab gjliultj E, ab lùfarj abafaltjs ka A, AG  y ab tefeõj fuastreb l 9 [efeõj ka E9 L

6

1 pjsubelas eb gjlgursj.

[efeõj ka A9 L 5

6

7 pjsubelas talal axparcalgce al fjkabjs bclaebas.

[efeõj ka AG9 L =

6

∝

 L L 5 = talal axparcalgce al asekæstge epbcgeke.

6

[efeõj fuasreb9 l

6

7.

Pesj 7. Lj axcsta clkapalkalgce altra bes abaggcjlas ka pjstubeltas9 Bes prjmemcbckekas ka sabaggcjler ul pjstubelta qua talhe axparcalgce al fjkabjs bclaebas vel gefmcelkj ka abaggc÷l al abaggc÷l . Pesj ;. Ckaltcocgegc÷l ka be vercemba ebaetjrce9 ^9 Lùfarj ka pjsubelas qua talal axparcalgce al fjkabjs bclaebas alra bjs ras sabaggcjlekjs al ojrfe ebaejrce.

 

 

Pesj 1. Kakuggc÷l ka be kcstrcmugc÷l 9 ^

Ncparhajf(14=4=) Ncparhajf(14=4=) .

Pesj ?. [rekugcr bes prahultes e ule axprasc÷l fetafåtcge ekagueke, gebguber y gjltaster9

]asp.9 Be prjmemcbckek ka qua ras sabaggcjlekjs, ka alra bjs gclgj pjsubelas, alhel axparcalgce al fjkabjs bclaebas as ka 0.? (?0%).

  Al asa gesj bj qua sa jmsarve qua bjs vebjras ka ^ sjl  x quã:). pjr bj elj sa pcka

e.

6

 (ºpjr

5,=,7

]asp.9 Be prjmemcbckek ka qua e bj fås kjs alhel axparcalgce al fjkabjs bclaebas as ka 0.30 (30.00%).

]asp.9 Wa aspare al prjfakcj qua = pjsubelas alhel axparcalgce al fjkabjs bclaebas, alra bjs 7 abahckjs ebaejrcefala ka ul jeb ka gclgj qua sa prasalerjl eb gjlgursj.

 

Gjfj ul kej ekcgcjleb pjkafjs, scl gjfprjfcsj ka raspjlkar e prahule ebhule, gebguber be kasvcegc÷l asålker ka ^9 Be kasvcegc÷l asålker kab lùfarj ka pjsubelas qua, al be fuasre, alkrål axparcalgce al fjkabjs bclaebas as ka 0.? pjsubelas.

8. Ql bjta ka 81 bevekjres gjltcala 1 al bes qua be vercemcbckek al ab hrjsjr ka be gcrguloaralgce ka be bevekjre as clegaptemba. Qle fuastre ka 50 bevekjres sa sabaggcjle eb ezer, scl raafpbezj. e. ºGuåb as be prjmemcbckek ka qua lclhule ka bes bevekjres clegaptembas astã al be fuastre:

ºGuåb as be prjmemcbckek ka qua lclhule ka bes bevekjres clegaptembas astã al be fuastre: ]asp.9 Wc ^  Wc ^  as  as ab lùfarj ka bevekjres clegaptembas, altjlgas

>. . (Epbcgegc÷l al Gcalgces ka be Webuk) Qle afprase afpbae e >00 njfmras faljras ka 11 eõjs. Wupjlhefjs qua ab 70% bbave ul fergekjr al ab grjfjsjfe fesgubclj qua clkcge ul feyjr rcashj pere be prasc÷l ertarceb ebte. Wc 50 njfmras al be afprase sa elebczel pere katarfcler ab fergekjr al asta grjfjsjfe,

 

e. ºguåb as be prjmemcbckek ka qua axegtefalta ul njfmra talhe ab fergekjr: m. ºguåb as be prjmemcbckek ka qua fås ka ulj talhe ab fergekjr:

3 . (Epbcgegc÷l al Gcalgces ka be Clhalcaræe) [eriates ka gcrguctjs cfprasjs sa gjbjgel al pruame ka oulgcjlefcaltj, kaspuãs ka nemar sckj kjtekes gjl gncps safcgjlkugtjras. Ql bjta gjltcala 5;0 teriates, y =0 sjl sabaggcjlekes scl sustctugc÷l, pere be pruame ka oulgcjlefcaltj.Wc =0 teriates sjl kaoagtujses, E) ºguåb as be prjmemcbckek ka qua eb faljs ule teriate kaoagtujse eperazge al be fuastre: M) Wc 1 teriates sjl kaoagtujses, ºguåb as be prjmemcbckek ka qua eb faljs ule teriate kaoagtujse eperazge al be fuastre:

E) ºGuåb as be prjmemcbckek ka qua eb faljs ule kabes teriates kaoagtujses asta al be fuastre:P(^ fuastre:P(^≡5º6 ≡5º6 5P(^60)P(^60)(=00) ( 5=0=0)(5;0=0)65=0!5=0!500!5;0!6 5=0=0)(5;0=0)65=0!5=0!500!5;0!60.0;=P(^≡5º6 0.0;=P(^≡5º6 5 0.0;=60.31 m) Wc ney gclgj teriates kaoagtujses,ºGuåb as be prjmemcbckek ka qua eb falj fa ljs s ul ulek eka a bes bes teri teriat ates es ka kaoa oagt gtuj ujse ses s ep eper eraz azge gel l al be fuas fuastr tre: e: P(^≡5º6 5P(^60)P(^60)(10) ( 571=0)(5;0=0)6 571=0)(5;0=0)6571!5=0!551!5;0!6 571!5=0!551!5;0!60.0;1P(^≡5º6 0.0;1P(^≡5º6 5 0.0;160.1; ([ajræe ka iuahjs) Ql astekj grae ule bjtaræe al be qua ? lùfarjs sjl sabaggcjlekjs eb ezer ka ;0, scl raafpbezj. Ql iuhekjr abcha sacs lùfarjs eltas ka qua, tefmcãl pjr abaggc÷l eb ezer, sa raebcga ab sjrtaj jocgceb.

e.ºGuåb as be prjmemcbckek ka qua bjs ? lùfarjs abahckj abahckjs s pjr ab  iuhekjr gjlguarkal gjlguarkal gjl bjs ? lùfarjs lùfarjs kab rasubtekj j jocgceb: ocgceb: ]asp.9 =.?017 50-8. ⋁

m.ºGuåb as be prjmemcbckek ka qua 1 ka bjs ? lùfarjs abahckjs pjr ab iuhekjr eperazgel al ab rasubtekj jocgceb: ]asp.9 1.75;8 50-1 ⋁

 

G. ºGuåb as be prjmemcbckek ka qua ; ka bjs ? lùfarjs abahckjs pjr ul iuhekjr eperazgel al ab rasubtekj jocgceb: ]asp.9 0.0=53=. K.Wc ul iuhekjr altre al ul sjrtaj geke safele, ºguåb as ab lùfarj asparekj ka safeles neste bes qua ab iuhekjr egcarte bjs sacs lùfarjs kab rasubtekj jocgceb: ]asp.9 Be prjmemcbckek ka egarter bjs sacs lùfarjs al ab sjrtaj ka ebhule safele as P(^6 ?) 6 =.?017 50-86 p. Wc kaschle ab lùfarj ka safeles neste jmtalar ab pbalj ka sacs lùfarjs egartekjs, altjlgas S sa kcstrcmuya hajfãtrcge gjl p 6 =.?017 50-8. Pjr bj teltj, A(S) 6 5/p 6 7 >7> 7>0 safeles (ebhj esæ gjfj 8 7>= eõjs). ⋁

⋁

3. (Gcalgces Mcjb÷hcges y Fakcjefmcaltebas) Al bjs astukcjs ka pjmbegc÷l mcjb÷hcge y fakcj efmcalta e falukj sa atcquatel y bcmarel aspagcas gjl ab ocl ka astcfer tefeõj y hrekj ka gcartes geregtaræstcges ka be pjmbegc÷l. Kcaz elcfebas ka ule katarfcleke pjmbegc÷l qua sa graa axtclte (j al axtclgc÷l) sjl gepturekjs, fergekjs y buahj bcmarekjs al ule rahc÷l katarfcleke. Clojrfegc÷l ockakchle eocrfe qua ney =1 elcfebas ka asta tcpj al be rahc÷l. Kaspuãs ka ul paræjkj ka tcafpj sa sabaggcjle ule fuastre ebaetjrce ka 51 ka elcfebas ka asta tcpj al ase rahc÷l. E)  ºGuåb as be prjmemcbckek ka qua 1 ka bjs elcfebas sabaggcjlekjs astãl fergekjs:

]9 0.=751 50. ([ajræe ka Prjmemcbckekas) Pere avcter be kataggc÷l al be ekuele, ul vceiarj buheras ? gjfprcfckjs ka astupaoegcaltas al ul oresgj gjl 3 pestcbbes ka vctefcles qua sjl scfcberas al epercalgce. Wc ab oulgcjlercj ka ekueles sabaggcjle e 7 ka bjs gjfprcfckjs eb ezer pere su elåbcscs, bj qua as be prjmemcbckek ka qua ab vceiarj sarå katalckj pjr pjsasc÷l cbaheb ka lerg÷tcgjs:

Wjbugc÷l9 L 6 3+? 651 jeb ka embaes e 6 ? embaes ka lerg÷tgj l 6 7 embaes sabaggcjlekes   x 6 0, 5, =, j 7 embaes ka lerg÷tgj 6 vercemba qua ljs clkcge ab lùfarj ka embaes ka lerg÷tgj qua sa puaka algjlrer eb sabaggcjler bes 7 embaes p(vceiarj sae errasekj pjr pjsasc÷l ka lerg÷tgjs) 6 p(ka qua alra bes 7 embaes sabaggcjlekes neye 5 j fås embaes ka lerg÷tgj)  

55. (Gcalgces Mcjb÷hcges) Ql kuaõj ka gese ? pbeltes ka mubmjs sabaggcjlekjs eb ezer ka ule geie qua gjltcala 1 mubmjs ka tubcpelas y lergcsjs ; mubmjs.

 

ºGuåb as be prjmemcbckek ka qua ãb safmr÷ = mubmjs ka lergcsjs y ; mubmjs ka tubcpål:

Wjbugc÷l9  Ketjs9 L6 3,l6 ?,d6 ;,x6= P(x6?)(;=) ( 3∝;?∝=)(3?)6 (;=) ( 1;)(3?)6 1/5; P(x6?) 6 0.7185;

5=. ([ajræe ka Fuastraj) Qle gjfpeõæe feluoegturare utcbcze ul pbel ka egaptegc÷l al bjs ertægubjs ka prjkuggc÷l eltas ka su alvæj eb gjfprekjr. Ab pbel gjlste ka kjs atepes9 Wa prapere pere ab alvæj ule geie ka =1 ertægubjs ka be gueb sa tjfe ule fuastre ka 7 y sa pruame astes ulckekas pere algjltrer kaoagtujses. Wc sa algualtre ebhulj kaoagtujsj, tjke be geie

as alvceke kabevuabte pere ab gjltrjb kab 500%. Wc lj sa algualtrel kaoagtujsjs, geie as alvceke eb gjfprekjr. ºGuåb as be prjmemcbckek ka qua ule geie qua gjltcala 7 kaoagtujsjs sae e. alvceke: ºGuåb as be prjmemcbckek ka qua ule geie qua gjltcala s÷bj 5 kaoagtujsj sae m. kavuabte pere su ravcsc÷l tjteb:

ule geie qua gjltcala 7 ertcgubjs kaoagtujsjs schlcocge qua ab vebjr ka x as garj L 6 =1.D 6 7.f 6 7.o(x)6(70) ( ==7)(=17)651;0=70060.??3 ==7)(=17)651;0=70060.??31m) 1m) Wc ule geie gjltcala ul ertcgubj kaoagtujsj schlcocge qua d 6 5, y sc sarahrase pere su ravcsc÷l schlcocge qua sa tuvj ãxctj al be sabaggc÷l ka asaertcgubj, pjr pjr teltj x 65.o(x)6(55) ( =;=)(=17)6=8?=7006 =;=)(=17)6=8?=70060.5= 0.5= 5=. (Gcalgces Wjgcebas) Wa astcfe qua ;.000 ka bjs 50.000 vjteltas rasckaltas al ule gcukek astål al gjltre ka ul luavj cfpuastj ka valtes. Wc 51 bjs vjteltas abahcmbas sjl sabaggcjlekjs eb ezer y sa bas pckc÷ su jpclc÷l, ºguåb as be prjmemcbckek ka qua fås ka 8 astãl e oevjr ab luavj cfpuastj:

 

 

 

 

57. (Gjltrjb fakcjefmcalteb) Ql jrhelcsfj humarlefalteb sjspagne qua ebhules afprases astål vcjbelkj bes bayas sjmra rahubegc÷l ka be gjltefclegc÷l gjl raspagtj eb kufpclh ka gcartj tcpj ka prjkugtj. _aclta afprases astål meij sjspagne, parj tjkes lj puakal sar clspaggcjlekes. Wupjlhefjs qua 7 ka bes afprases astål vcjbelkj bes bayas. e. ºGuåb as be prjmemcbckek ka qua al be clspaggc÷l ka 1 afprases lj algualtra vcjbegcjlas:

]9 0.7335 m. ºGuåb as be prjmemcbckek ka qua ab pbel parfcte algjltrer kjs vcjbegcjlas:

]9 0.575?