ESTADISTICA EXamen Final 3 CICLO

 

 HC[O

  ]WGMO GTD]N[O O]O GQOIGH @NHOB TGIGT[]G BGD[NPC =5?> — N

[GIOT @NHOB: [ombos kg @rgdughdno @rgdughdno:: Dorodtgréstn Dorodtgréstndos dos  

=.  [ombo kg dchtnhfghdno: Urcmomnbnkokgs 4.  Knstrnmudnôh kg Ucnssch ;.  Knstrnmudnôh Hcriob 7.  Ickgbc kg ]gfrgsnôh Bnhgob Tnipbg. 0.  Tgrng Drchcbôfndo

Gstokéstndo Opbndoko o bo fgstnôh Giprgsornob  Osnfhoturo gvobuoko:  Opgbbnkcs y hcimrgs kgb gstuknohtg

Dôknfc:

T =O5k?i>n-hNnst GgsdiuggsbotrgUrocd`tgusoncb:hob: strrodnôh: ( ) Hgfcdncs Nhtgrhodnchobgs ( ) ]gdu durrscs Auiohcs ( ) Iorlgtnhf ( ) Urc`gscr G Gvvobuokcr: Dostnbbbbcc ]c ]csornc Bo Bouro ^s ^somgb Tgddnôh: 5;I5;  Oubo: Bom=O [urhc: Ioÿoho Kurodnôh kg bo prugmo >5 inhutcs @gdao kg gvobuodnôh ?5/50/?> @gdao kg kgvcbudnôh kgb ?6/50/?> gxoigh Hcto: Gb gstuknohtg qug hc gstuvngro prgsghtg gh gb oubo gh gb icightc kg bo kgvcbudnôh kg bcs gxïighgs dcrrgfnkcs pcr gb prc`gscr, pgrkgrï su kgrgdac o rgdboior. @nrio kgb obuihc: Urgfuhtos:

?. DCHCDNINGH[CT (4 puhtcs) Doscs:

Dosc N: Tg bbgvo o domc uh gstuknc scmrg gb sgrvndnc kg tgbg`chéo Icvnstor [ctob, gh bos `oinbnos qug rgsnkgh gh gb knstrntc knstr ntc kg Inro`bcrgs, Inro`bcrgs, dchsnkgrohkc dchsnkgrohkc

Pornombg Fostc ighsuob kgb sgrvndnc

gb fostc ighsuob kgb sgrvndnc. Dosc NN:

Húigrc kg bboiokos poro Gh bo nh nhvvgstnfodnôh poro gb scbndntor uh prîstoic. bohzoinghtc kg uho doipoÿo kg prîstoics o sus dbnghtgs kg dngrto ghtnkok mohdorno, igknohtg gb Dobb dg dght htgr gr qu qung nghh sg gh ghdo dorf rfoo kg rg rgob obnz nzor or bboi bboiok okos os igkn igknoh ohtg tg gb tg tgbg bgcp cpgr grok okcr cr o sus sus kn kn`g `grg rght htgs gs dbng dbnght htgs gs,, sg kgsg kgsgoo gs gstntnio iorr gb húigrc kg bboiokos kg dcbcdodnchgs gh uh kéo.

Dosc NNN:

[npc kg béhgo kg

Dbosn`ndodnôh Pornombg duohtntotnvo dchtnhuo

Igkndnôh ]ozôh

Whnkok kg ohïbnsns Bo `oinbno qug rgsnkg gh gb Knstrntc kg Inro`bcrgs.

Pornombg duohtntotnvo knsdrgto

]ozôh

Gb dbnghtg kg bo gghhtnkok mohdorno qug scbndnto uh prîstoic.

Pornombg

Hcinhob

Gb dbnghtg kg bo

 

Who hugvo giprgso kg knspcsntnvc prg`grghdno kgb usuornc. iôvnb gstï gstuknohkc bos pcsnm snmnbnkokgs kg nhfrgso sorr ob igrdok igr dokcc pgruoh pgruohc, c, poro poro tob g`gdtc g`gdtc ghdorfo o uho giprgso gh ghdu dugs gsto tokc kcro ro kg kgbb igkn igkncc bbg bbgvg vg o domc gb gstuknc kg bcs tnpcs kg béhgo (pcst pofc, prg-.pofc) kg prg`grghdno kgb usuornc. =. DCI ]GHTNÔH (4 puhtcs)

   

duobntotnvo

giprgso tgbg`ôhndo qug scbndnto uho béhgo kg tgbî`chc.

Dosc: [nghko Outcsgrvndnc.

Tg kgsgo rgobnzor uh gstuknc scmrg dngrtos dorodtgréstndos kg bcs dbnghtgs kg bos [nghkos "Ubozo Pgo", kgmnkc o bcs rgdboics pcr bcs tngipcs kg kgicro qug prgsghtoh poro sgr otghknkcs gh dojo. Bcs dbnghtgs nhsotns`gdacs pcr gb sgrvndnc rgfnstroh sus qugjos gh gb ‒Bnmrc kg ]gdboiodnchgs’. Tg dchsnkgrô tcior uho iugstro snfhn`ndotnvo kg gstcs dbnghtgs kg toioÿc h9 65. Bos qugjos gh gb bnmrc kg rgdboiodnchgs: Urckudtcs dtcs snh dôknfc kg _ugjos: Bos qugjos qug rgobnzoh bcs dbnghtgs. ?9Kgicro gh gb pofc kg torjgtos kg drîkntc< =9Urcku sgfurnkok< 49Ucdcs dojgrcs knspchnmbgs, ;9Hc aoy snstgio poro gb pofc kg sgrvndncs< 79Iudac tngipc poro rgscbvgr bcs grrcrgs kg bcs dojgrcs< 09 Dcbos iuy borfos.

Mosg kg Kotcs: MKSOutcsgrvndnc.Tov o) GBOM GBOMC] C]GG GB KN KNOF OF]O ]OIO IO KG O] O]G[ G[C: C:

[ombos kg ]gdughtcs Kgsdghkghtgs Ucrdghtojg @rgdughdno Pïbn Pï bnkc kc

Kgic Kg icro ro gh gb po pofc fc kg

Ucrdghtojg

oduiubokc

?1

=7,6

= 7 ,6

Ucdcs dojgrcs knspchnmbgs

?7

=?,;

; 6 ,?

Urckudtcs snh dôknfc kg

?4

?1,0

0 7 ,6

?=

?6,?

1 = ,>

>

?=,>

> 7 ,6

4

; ,4

?55,5

65

?55,5

torjgtos kg drîkntc

sgfurnkok Iudac tngipc poro rgscbvgr bcs grrcrgs kg bcs dojgrcs Hc aoy snstgio poro gb pofc kg sgrvndncs Dcbos iuy borfos [ctob

 

m) ³Duïbgs ³Duïbgs sch sch bos qugjos qug kgmg kgmg igjcror igjcror bo dobnkok dobnkok kgb sgrvndnc sgrvndnc3. 3. ## ?. =. 4. ;.

 

_ugjo _ugjoss qug qug bo tngh tnghko ko dci dcigr grdno dnobb tntngh ghgg qug qug igjc igjcro ror. r. Kgic Kgicro ro gh gb pofc pofc kg torj torjgt gtos os kg dr drîk îkntntc. c. Ucdcs do dojgrcs kn knspchnmbgs. Ur Urck ckud udtc tcss snh snh dôkn dôknfc fc kg sg sgfu furn rnko kok. k. Iuda Iudacc tngi tngipc pc por poroo rgsc rgscbv bvgr gr bcs pr prcm cmbg bgio ioss kg bc bcss dojg dojgrc rcs. s. 4. O BNDODNÔH (4 puhtcs) Gh uho giprgso aoy 67 gipbgokcs, kg bcs duobgs ;5 sch ghdorfokcs kg iordo y 47 sch okinhnstrotnvcs. Kg gstcs gipbgokcs scbc ;6 usoh Tiortpachg kg bcs duobgs 47 sch ghdorfokcs kg iordo. Tn sg sgbgddncho uh gipbgokc ob ozor:

Knspcsntvc Iôvnb  

Tiorpachg

Okinhnsrotvcs

[cob

47 47

?=

;6

7

=4

=1

;5

47

67

 

Hc usoh Tiorpachg  

[cob

Iordo

o.- ³Duïb gs prcmomnbnkok qug gb gipbgokc sgo gb ghdorfokc kg iordo y uso Tiortpachg3. 47 67

U(IT)9 95.;6 m.- ³Duïb gs bo prcmomnbnkok qug gb tromojokcr sgo okinhnstrotnvc c hc uso Tiortpachg3   U(OWHT)9U(O)+U(HT)-U(OHT)9

 

947/67+=1/67-=4/67

U(OWHT)9U(O)+U(HT)-U(OHT)9

5.7444

;. OHÏBNTNT (4 puhtcs). Gh uh vgaédubc nhkustrnob gb húigrc kg pnhdaozcs snfug uho knstrnmudnôh kg Ucnssch, dch igkno kg 5.4 pcr doko 75 555 lnbôigtrcs. Té uh vgaédubc nhkustrnob rgdcrrg ?55 555 lnbôigtrcs. Tg pnkg: o.- Nkghtn`nqug bo vornombg obgotcrno y dcic sg knstrnmuyg: Pornombg obgotcrno Q9 Húigrc kg pnhdaozcs

Q

Knstrnmudnôh

(5.4*755559?7555)

m.- Urcmomnbnkok kg qug tghfo pcr bc ighcs kcs pnhdaozc.  

U\Q 89=

Y 9?

7. TÉH[GTNT (; puhtcs). Tg tnghg bo knstrnmudnôh kg bos gkokgs kg tckcs bcs gstuknohtgs kg bo `odubtok kg Dnghdnos Okinhnstrotnvos y ]gdurscs Auiohcs kg dngrto uhnvgrsnkok portndubor kg Bnio. Ubohtgohkc qug sg scspgdao qug bos gkokgs kn`ngrgh kg =7 oÿcs. Tg dchsnkgro uho iugstro obgotcrno kg h9;5 gstuknohtgs y ghdchtroics qug bo gkok prcigknc gs kg ==.7 oÿcs, dch uho kgsvnodnôh gstïhkor kg ;.7 oÿcs. Osuio uh 95.57

Kgtgrinhg bo rugmo kg Anpôtgsns poro bo igkno pcmbodnchob: ]gfbo kg bcs 7 poscs Uosc?: Anpôtgsns

Uosc=: Hnvgb kg Tnfhn`ndodnôh

Ac:9=7 A?:=7  

95.57

 

Uosc4: Gstokéstndc kg Urugmo (Z) Gstokéstndc kg Urugmo (ZD)

Z Dobdubokc

(  xx  β ) ∝

9

( )  T

√ h

]ggipbozohkc:

Z Dobdubokc

( ==.7

∝

9

=7

( )

 

)

4.7?;

9∝

; .7

√ ;;55

Uosc;: @criubor bo ]gfbo kg Kgdnsnôh.

Knstrnmutnch Ubct Hcriob, Igoh95, TtKgv9? 5.;

5.4

    y      t       n     s     h 5.=     g       K

5.?

5.5=7 5.5

5.5=7 -?.>05

5

?.>05

Q

ZDobdubokc9-4.7?;, Ac  ]]

Uosc7: Dchdbusnôh:

Aoy gvnkghdnos su`ndnghtgs poro rgdaozor Ac, pckgics dchdbunr qug bos gkokgs kn`ngrgh kg =7 oÿcs, osuinghkc uh hnvgb kg dch`nohzo kgb >7%.

0. POBC]ODNÔH (; puhtcs). Tg kgsgo nhvgstnfor bo nhtghsnkok kg bo rgbodnôh ghtrg bos dobcréos pcr ?= chzos béqunkos y gb obdcacb pcr vcbuigh ( gh %), gh gb prcdgsc kg prckuddnôh kg uho iordo rgdchcdnko kg dgrvgzo o hnvgb hodnchob. Bcs snfunghtgs rgpcrtgs kgb I]BT:

Mosg kg Kotcs: DgrvgzoSdobcréos SObdcacb.Tov. ]gpcrtg ?: ]gsuigh kgb ickgbc Ickgbc ?

 

] duokrokc

Grrcr gstïhkor 

]

] duokrokc

ojustokc

kg bo gstniodnôh

,>?;o

,140

,14?

,=;601

o. Urgkndtcrgs: (Dchstohtg), Dobcréos pcr ?= chzos béqunkos

]gpcrtg =:

OHCPOo Tuio kg Ickgbc ?

Igkno

duokrokcs

fb

duokrïtndo

]gfrgsnôh

? 5 ,4 4 6

?

?5,446

]gsnkuc

= ,5 = ;

44

,5 0 ?

[ctob

? = ,4 0 =

4;

o. Pornombg kgpghknghtg: Obdcacb pcr Pcbuigh (gh %)

 

@

Tnf.

?01,754

,555m

 

m. Urgkndtcrgs: (Dchstohtg), Dobcréos pcr ?= chzos béqunkos

]gpcrtg 4:

Dcg`ndnghtgso Dcg`ndnghtgs Dcg`ndnghtgs hc gstohkornzokcs Ickgbc ?

(Dchstohtg)

 

Dobcréos pcr ?= chzos

M

Kgsv. Grrcr

?,;=7

,=;0

,5=4

,55=

gstohkornzokcs Mgto

,>?;

t

Tnf.

7,61?

,555

?=,>1?

,555

béqunkos o. Pornombg kgpghknghtg: Obdcacb pcr Pcbuigh (gh %)

?) @criu @criubg bg ggbb ic ickgbc kgbc kg rrgfrg gfrgsnôh snôh bnhg bnhgob ob ssnipb nipbg. g. ^ 9 ν5 + ν? Q + gn

Gduodnôh gstnioko: ³

^ 9?.;=7 + 5.=4∖ Q 

Nhtgrprgtodnôh: o9 Nhtgrdgptc gh bo crkghoko. (5, ?.;47)< m9 Bo pghknghtg gs pcsntnvo, bo rgbodnôh gs knrgdto o igknko qug Q ouighto ^ toimnîh ouighto. Ucr doko uhnkok qug ouightg Q, ghtchdgs ^ qugko ouightoko gh gb vobcr kg su pghknghtg.

=) Gstukng bo okgduodnôh kgb ickgbc igknohtg gb dcg`ndnght dcg`ndnghtgg kg dcrrgb dcrrgbodnôh, odnôh, gb dc dcg`ndnghtg g`ndnghtg kkgg kgtgrinhod kgtgrinhodnôh nôh y prugmo kg anpôtgsns.

o) Dcg`nd Dcg`ndngh nghtg tg kg Dc Dcrrg rrgbod bodnôh nôh:: r 95.>?; 95.>?; Nhtgrprgtodnôh:

Gxnstg uho `ugrtg rgbodnôh ghtrg bos vornombgs Q g ^, dch uh dcg`ndnghtg kg dcrrgbodnôh 5.>?; dgrdohc o ?. m) rugmo kg anpôtgsns: ?) Ubo Ubohtg htgoin oinght ghtcc kg bo aanpô npôtgs tgsns: ns: A5: ?95 Gb I]BT hc gs okgduokc o Hnvgb pcmbodnchob. A?: ?  5 Gb I]BT gs okgduokc o Hnvgb pcmbodnchob. =) Hnvg Hnvgbb kg ssnf nfhn hn`n`ndo dohd hdno no ο 9 7% 4) Gs Gsto toké kést stnd ndcc kkgg ppru rugm gmoo Urugmo @: OHCPO

 

@Dobdubokc9?01.574 @[omubokc9 ;.?; Dciporor @Dobdubokc Ps @[omubokc

;) Kgdnsnôh: Aoy gvnkghdnos su`ndnghtgs poro rgdaozor bo Anpôtgsns Hubo , pcr tohtc o uh hnvgb kg snfhn`ndohdno Kg 5.57, dchdbunics qug gb I]BT gs oprcpnokc o hnvgb pcmbodnchob.