Distribuciones Probabilisticas: Variable Aleatoria: Posibles Valores

 

MNW][NKVGNJLFW Y[JKOKNBNW]NGOW Whfnbby [jsobfs Ejlzïbfz ‗ ??97

?. Vlo pfrsjlo gjcpro bo bjtfrão gomo sfcolo o bj borej mfb oÿj (6; sfcolos), guflto fb lñcfrj mf vfgfs quf eol÷ obej. Gjl kosf fl fstj, ºGuïb fs bo vornokbf obfotjrno: ^ ºguïbfs sus pjsnkbfs vobjrfs: Tornokbf obfotjrno1 Yjsnknbnmom mf quf bo pfrsjlo eolf j pnfrmo fl fb aufej, mfltrj mf bo

golmom mf vfgfs quf bj gjcprj (6; sfcolos). Yjsnkbfs vobjrfs1 Eolor (?) j pfrmfr (;). Mfltrj mf bos sfcolos. ;. Nmfldgo guobfs vornokbfs sjl obfotjrnos mnsgrftos y guobfs obfotjrnos gjlluos o. Fb lñcfrj mf pfrsjlos quf fstïl colfaolmj fl fstf cjcfltj fl Gjbjckno1 G jbjckno1 Tornokbf obfotjrno mnsgrfto.

k. Fb pfsj mfb jrj obcogflomj fl Djrt @ljx1 Tornokbf obfotjrno gjlluo. g. Bo obturo mfb ovn÷l cïs erolmf gjlstrunmj hosto fb cjcfltj1 Tornokbf obfotjrno gjlluo. m. Fb lñcfrj mf prjpnftornjs quf hngnfrjl rfgbocogn÷l mf su sfeurj outjcjvnbãsgj mfknmj o ul oggnmfltf1 Tornokbf obfotjrno mnsgrfto. f. Fb fcpj lfgfsornj poro vnoaor mf Kjejtï o Yorns1 Tornokbf obfotjrno gjlluo. 7. Tfrndquf sn bo nljrcogn÷l sucnlnstromo fl bos sneunfltfs tokbos gjrrfspjlmf o ulo mnstrnkugn÷l prjkoknbãsgo, sn bj fs flgufltrf bo cfmno y mfsvnogn÷l1

o. ]rfs hjckrfs hjckrfs flfl flfl ul trostjrl trostjrlj j eflîg eflîgj j rfbognjlom rfbognjlomj j gjl fb grj grjcjsjc cjsjco o X, gomo ulj ulj fleflmro fleflmro ul hnaj. Bo vornokbf obfotjrno x fs fb lñcfrj mf hnajs mf bjs trfs hjckrfs quf hfrfmol fb trostjrlj eflîgj rfbognjlomj gjl fb grjcjsjco X. (β 3 ?,6 y χ 3 9,>)

 β3 (? Õ 9.756 )+ ( ; Õ 9.756 ) + ( 7 Õ 9.?;6 ) 3?,6 ;

χ 

3

P (( 9

∛

;

?.6 ) Õ 9.?;6

) ( ( ? +

∛

;

?.6 ) Õ 9.756

) ( ( ; +

∛

;

?.6 ) Õ 9.756

χ 3∑ 9.56 9.5639.>

) (( 7 +

∛

;

?.6 ) Õ 9.?;6

)S

3

9.56

 

k. Vlo fcprfso fcprfso oîrfo flf flf bo pjbãgo pjbãgo mf sjkrf vflmfr vflmfr sus vufbjs. vufbjs. Bo vornokb vornokbf f obfotjrno obfotjrno fstï rfprfsfltomo pjr fb lñcfrj mf posoafrjs quf lj pufmfl okjrmor mfknmj o quf hoy cïs posoafrjs quf osnfltjs. Bo prncfro gjso quf sf pufmf ljtor fs quf lj guflto gjl tjmos bos gjlmngnjlfs mf ulo gjlmngn÷l prjkoknbãsgo pufs bo suco mf tjmos sus prjkoknbnmomfs lj mo ulj. 9.96? + 9.?=? + 9.;5= + 9.77? + 9.?85 39.>8= Wnl fckorej, ob sfr bo rfspufsto lj tol obfaomo prjgfmfrî prjgf mfrî o rfobnzor fb prjgfmncnfltj ljrcob poro vfr fb pjsnkbf rfsubtomj.

 β3 (? Õ 9.?=? )+ (; Õ 9.;5= ) + ( 7 Õ 9.77? ) + ( = Õ 9.?85 )3;.=7 ;

χ 

3

P (( 9

∛

;

;.=7 ) Õ 9.96?

) ( ( ? +

∛

;

;.=7 ) Õ 9.?=?

) ( ( ; +

∛

;

;.=7 ) Õ 9.;5=

) (( 7 +

∛

;

;.=7 ) Õ 9.77?

) (( = +

∛

;

;.=7 ) Õ 9.?8

χ 3∑ ?.;9 ?.;93?.9> ]flnflmj fl guflto bo sneunfltf tokbo quf mfsgrnkf bjs rfsubtomjs 8 vïstoejs mf eunsoltfs vfrmfs.

mf

=. Gobgubf bo cfmno y mfsvnogn÷l fstïlmor mf bjs motjs sucnlnstromjs (β 3 4 y χ 3 ?,;)

 β3 ( 9 Õ 9 ) + ( ? Õ 9 )+ ( ; Õ 9.99= ) + ( 7 Õ 9.9;7 ) + ( = Õ 9.985 ) + ( 6 Õ 9.;98 ) + ( 4 Õ 9.7?? ) + ( 5 Õ 9.;45 )+ ( 8 Õ 9.?99 )3 4 ;

χ  (?( 9.=>=43) Õ?.;9 ) χ 3 ∑ ?.=>=

P

∛

+

(( ?

∛

4) Õ 9

) ( ( ; 4 ) +

∛

Õ 9.99=

) (( 7 +

∛

4 ) Õ 9.9;7

) (( = +

∛

4 ) Õ 9.985

) ( (6 +

∛

4 ) Õ 9.;98

6. ]flnflmj fl guflto bo rfebo prïggo mf bos mfsvnognjlfs poro nmfldgor ul rolej mf vobjrfs quf gjltfleol fb lñcfrj gjcñl mf eunsoltfs gjl vonlos vfrmfs. ºGjl kosf fl bjs rfsubtomjs, fs nlusuob jktflfr sjbj ul eunsoltf gjl vonlo vfrmf: Fxpbnquf Molmj kosf quf sf mfdlf gjcj rfsubtomj nlusuob oqufbbjs fl bjs quf bo coyjrão mf vobjrfs lj sf flgufltros o cos mf mjs mfsvnognjlfs mf bo cfmno, pjr bj quf sf mftfrcnlo quf ul vobjr gjcñl mfkf fstor o ¿;χ mf β. Wf pjmrão gjlgbunr quf ob fstor 9 pjr ufro mfb rolej, jktflfr ul sjbj eunsoltf gjl vonlo vfrmf fs nlusuob. 4. Gobgubf bo prjkoknbnmom mf jktflfr 5 eunsoltfs gjl vonlos vfrmfs Bo prjkoknbnmom fstï fxpufsto fl bo tokbo y fs mf 9.;45

;

;

;

;

;

;

; 3

) (( 4 +

∛

4) Õ

 

5. Gobgubf bo prjkoknbnmom mf jktflfr 6 j cïs eunsoltfs gjl vonlos vfrmfs. (Y 3 9,884)

 Y3 9.;98 + 9.7?? + 9.;45 + 9.?9939.884 8. Fxnstf ulo prjkoknbnmom mf 9.?>?> mf quf bo sfrnf culmnob mf kînskjb murf guotrj aufejs, ulo prjkoknbnmom mf 9.;?;? mf quf murf 6 aufejs, ulo prjkoknbnmom mf 9.;;;; mf muror sfns aufejs y mf 9.7575 mf bbfeor hosto fb aufej snftf.

o. ºBo nljrc nljrcogn÷l ogn÷l mfsgrnkf mfsgrnkf ulo ulo mnstrnku mnstrnkugn÷l gn÷l mf mf prjkoknbn prjkoknbnmom: mom: Wn, mfknmj o quf ulo mnstrnkugn÷l prjkoknbãsgo sf mfdlf gjcj bo prjkoknbnmom mf gomo vobjr mf

bo vornokbf obfotjrno y fstf fs fb gosj mfb ogjltfgncnfltj fxpufstj pufs, cufstro bjs rfsnbtomjs pjsnkbfs quf pufmf tflfr ulo vornokbf. k. Gobgubf Gobgubf bo cfmno y bo mfsvno mfsvnogn÷l gn÷l fstïlmor fstïlmor mfb lñcfrj lñcfrj mf aufejs aufejs fl bo Wfrnf Wfrnf Culmnob Culmnob mf Kînskjb. Kînskjb. (β 3 6,8 y χ 3 ?,?)  β3 ( = Õ 9.?>?> ) + ( 6 Õ 9.;?;? ) + ( 4 Õ 9.;;;; ) + ( 5 Õ 9.7575 )36.55 ;

χ 

3

P (( =

∛

;

6.55 ) Õ 9.?>?>

) ( (6 +

∛

;

6.55 ) Õ 9.;?;?

) ( ( 4 +

∛

;

6.55 ) Õ 9.;;;;

) (( 5 +

∛

;

6.55 ) Õ 9.7575

χ 3∑ ?,79= ?,79=3?,? g.

ºWfrï nlusu nlusuob ob quf ul fqunpj fqunpj ‒orrosf– ‒orrosf– ob eolor eolor guotrj guotrj aufe aufejs: js: ºYjr ºYjr quî: quî: ]flnflmj fl guflto quf ul vobjr gjcñl mfkf fstor o ¿;χ mf β (cfmno orntcîgo) y fsto fs neuob o 9.5?>, sn sf ffgtuo bo rfebo rf ebo mf bos mfsvnognjlfs ljs morfcjs guflto mf quf sfrão nlusuob quf fb fqunpj eoloro guotrj aufejs.

>. Fxnstf ulo prjkoknbnmom mf 9.>>84 mf quf ul hjckrf mf 79 oÿjs mf fmom, fbfenmj f bfenmj ob ozor, sjkrfvnmo muroltf fb oÿj. Bo osfeuromjro gjkro V$?4? pjr osfeuror o ul hjckrf quf sjkrfvnvo muroltf fb oÿj. Wn fb hjckrf lj sjkrfvnvf fsf oÿj, bo p÷bnzo poeo V$?99999 pjr bo cufrtf. o. ºguïbfs sjl bjs vobjrfs gjrrfspjlmnfltfs gjrrfspjlmnfltfs o bjs mjs fvfltjs mf sjkrfvnvnr y lj sjkrfvn sjkrfvnvnr vnr fl fb oÿj: (?4?0 >>87 Wjkrfvnvnr gjrrfspjlmf o -?4?  

?4? Õ 9.>>84 3∛?49.55=43∛ ?4?Lj sjkrfvnvnr gjrrfspjlmfr o >>87>, mfknmj o quf sf rfsto fb prfgnj mf bo p÷bnzo o bj quf poeo fl gosj mf cufrtf1 ?99999∛?4? 3>>87> ∛

k. Wn ul hjckrf hjckrf mf 79 oÿjs oÿjs gjcpro gjcpro bo p÷b p÷bnzo, nzo, ºg ºguïb uïb sfrão sfrão su vobjr vobjr fspfromj: fspfromj: F3-;? F3-;?  F 3

g.

P (

) ( >>87> Õ (? ∛9.>>84 ) ) S3∛;?

∛ ?4? Õ 9.>>84 +

ºBo gjcpoÿão gjcpoÿão mf sfeur sfeurjs js pjmrão pjmrão fspfror fspfror jktflfr jktflfr ulo e eololgn ololgno o mf ulo erol erol golmom golmom mf p÷bnzos p÷bnzos mf fsf pj: ºYjr quî:

) S

3

?,79=

 

Wn pjmrão fspfror ulo eololgno pufs, tflnflmj fl guflto quf bo prjkoknbnmom mf quf cufro opflos fs mf ul 9.99?= (?-9.>>84), bo prjkoknbnmom mf quf tfleo quf poeor ?99999 fl gosj mf quf bo pfrsjlo cufro sjl cuy koaos.