problemas-fundamentos+de+probabilidad-2p

4
'(3$57$0(172 '( (67$'Ë67,&$ ( ,2 *5$'2 (1 &,(1&,$6 $0%,(17$/(6 (67$'Ë67,&$ 3UREOHPDV )XQGDPHQWRV GH 3UREDELOLGDG (MHUFLFLR &RQVLGHUDQGR HO H[SHULPHQWR GH ODQ]DU XQD PRQHGD HTXLOLEUDGD HVWDEOHFHU HO iOJHEUD GH VXFHVRV IRUPDGD SRU ODV SDUWHV GHO HVSDFLR PXHVWUDO \ FDOFXODU OD SUREDELOLGDG GH REWHQHU FDUD FXDQGR UHDOL]DPRV XQ ODQ]DPLHQWR (MHUFLFLR 6L VH UHDOL]DQ ODQ]DPLHQWRV GH XQD PRQHGD HTXLOLEUDGD &DOFXODU ODV SUREDELOLGDGHV GH 2EWHQHU XQD FDUD 1R REWHQHU QLQJXQD FDUD 2EWHQHU DO PHQRV XQD FDUD 2EWHQHU FUXFHV (MHUFLFLR (Q HO ODQ]DPLHQWR GH XQ GDGR ³SHUIHFWR´ WRGDV ODV FDUDV WLHQHQ OD PLVPD SRVLELOLGDG GH VDOLU HQ FDGD ODQ]DPLHQWR &DOFXODU OD SUREDELOLGDG GH REWHQHU XQ &DOFXODU OD SUREDELOLGDG GH REWHQHU XQ R XQ &DOFXODU OD SUREDELOLGDG GH REWHQHU XQ UHVXOWDGR SDU &DOFXODU OD SUREDELOLGDG GH REWHQHU XQ PHQRU R LJXDO TXH &DOFXODU OD SUREDELOLGDG GH REWHQHU XQ UHVXOWDGR VXSHULRU D &DOFXODU OD SUREDELOLGDG GH REWHQHU XQ UHVXOWDGR SDU \ QR PD\RU D &DOFXODU OD SUREDELOLGDG GH REWHQHU XQ UHVXOWDGR SDU R LQIHULRU R LJXDO D 6ROXFLRQHV 8WLOL]DUHPRV OD UHJOD GH /DSODFH HQ OD REWHQFLyQ GH ORV UHVXOWDGRV GH HVWH HMHUFLFLR GDGR TXH VH WUDWD GH XQ H[SHULPHQWR DOHDWRULR FRQ XQLYHUVR ILQLWR \ HOHPHQWRV HTXLSUREDEOHV 6XFHVR $³REWHQHU XQ ´ ^` 3$ 6XFHVR %³REWHQHU XQ R XQ ´ ^ ` ^`8^` 3% 2EVHUYDU TXH SRGUtD REWHQHUVH XVDQGR 3^`3^` 6XFHVR &³REWHQHU XQ UHVXOWDGR SDU´ ^ ` ^`8^`8^` 3& 6XFHVR '³REWHQHU XQ UHVXOWDGR PHQRU R LJXDO TXH ´ ^ ` 3' 2EVHUYDU TXH SRGUtD REWHQHUVH XVDQGR TXH 'ȍ% 6XFHVR (³REWHQHU XQ UHVXOWDGR PD\RU TXH ´ ^ ` HV GHFLU (% 3( 'HO PLVPR PRGR SRGUtD REWHQHUVH XVDQGR TXH ( ȍ' D 3(±3'± 6XFHVR )´REWHQHU XQ UHVXOWDGR SDU \ QR PD\RU D ´^` 3) 2EVHUYDU TXH HVWH VXFHVR HV OD LQWHUVHFFLyQ GH & \ ' )&ŀ' (O VXFHVR ³REWHQHU XQ UHVXOWDGR SDU R LQIHULRU R LJXDO D ´ HV OD XQLyQ GH ORV VXFHVRV & \ ' &8'^` 3&8' 2EVHUYDU TXH GHO DSDUWDGR DQWHULRU WHQHPRV HO VXFHVR LQWHUVHFFLyQ GH & \ ' SRU OR TXH WDPELpQ SXHGH REWHQHUVH PHGLDQWH OD SURSLHGDG 3&8'3&3'±3&ŀ' (MHUFLFLR 6H UHDOL]DQ ODQ]DPLHQWRV GH XQ GDGR &DOFXODU ODV VLJXLHQWHV SUREDELOLGDGHV /RV UHVXOWDGRV GH ORV GRV SULPHURV ODQ]DPLHQWRV VHDQ \ FRQVHFXWLYDPHQWH /RV UHVXOWDGRV GH ORV GRV SULPHURV ODQ]DPLHQWRV VHDQ \ LQGLVWLQWDPHQWH 2EWHQHU H[DFWDPHQWH XQ \ XQ HQ DOJXQR GH ORV ODQ]DPLHQWRV (O VXFHVR $ HVWi FRQVWLWXLGR SRU WRGRV ORV ODQ]DPLHQWRV SRVLEOHV HQ ORV TXH HO UHVXOWDGR HV GH OD IRUPD ³[\´ \ HO VXFHVR % SRU WRGRV ORV GH OD IRUPD ³[\´ &DOFXODU OD SUREDELOLGDG 3$8% 6ROXFLRQHV 2EVHUYDU TXH FDGD UHVXOWDGR GHO H[SHULPHQWR HVWi IRUPDGR SRU FXDWUR FRPSRQHQWHV RUGHQDGDV XQD SRU FDGD ODQ]DPLHQWR $Vt DO HVSHFLILFDU VyOR ORV GRV SULPHURV HO VXFHVR SHUPLWH FXDOTXLHU YDORU SRVLEOH SDUD HO WHUFHU \ FXDUWR ODQ]DPLHQWR HV GHFLU $^[\ [ \ FXDOTXLHU YDORU GHO GDGR` 3[\FDVRV IDYRUDEOHV FDVRV SRVLEOHV 3[\ 8 [\ 3[\ 3[\ SXHV VRQ VXFHVRV GLVMXQWRV 6L TXHUHPRV VyOR XQ \ VyOR XQ HQ HO UHVXOWDGR GH ORV FXDWUR ODQ]DPLHQWRV SULPHUR YDPRV D YHU GH FXDQWDV PDQHUDV SRGHPRV FRORFDU HO \ HO HQ HO UHVXOWDGR 3DUD HOOR YDPRV D YHU FyPR FRORFDU SULPHUR HO \ OXHJR FRORFDGR pVWH FRORFDU HO 3DUD HO KD\ ³VLWLRV´ FXDOTXLHUD GH ORV FXDWUR ODQ]DPLHQWRV \ SDUD HO TXHGDUiQ VLWLRV GDQGR XQ WRWDO GH SRVLELOLGDGHV &RPR HO SDSHO GHO \ HO VH SXHGHQ LQWHUFDPELDU GDQGR OXJDU D UHVXOWDGRV GLIHUHQWHV HQ WRWDO KDEUi UHVXOWDGRV GLIHUHQWHV HQ ORV TXH KD\ XQ \ XQ (Q ORV GRV ODQ]DPLHQWRV UHVWDQWHV SXHGH REWHQHUVH FXDOTXLHU UHVXOWDGR HQWUH ODV FDUDV \ SRU WDQWR VHUiQ HQ WRWDO UHVXOWDGRV $Vt HQ WRWDO WHQGUHPRV [ UHVXOWDGRV IDYRUDEOHV (QWRQFHV OD SUREDELOLGDG SHGLGD HV 3$ 6L $^[\ [\` \ %^[\ [\` HQWRQFHV $ŀ% \ SRU WDQWR OD SUREDELOLGDG GH OD XQLyQ HV 3$8%3$3% (MHUFLFLR (O VXFHVR VHJXUR HVWi IRUPDGR SRU ODV OHWUDV D E F G \ H $ SDUWLU GH HVWDV VH YDQ D IRUPDU DJUXSDPLHQWRV GH OHWUDV FRPR ³EDG´ D ORV TXH GHQRPLQDUHPRV ³SDODEUDV GH OHWUDV´ &DOFXODU OD SUREDELOLGDG GH TXH XQD SDODEUD FRQWHQJD OD OHWUD D H[DFWDPHQWH YH] &DOFXODU OD SUREDELOLGDG GH TXH XQD SDODEUD FRQWHQJD OD OHWUD E DO PHQRV XQD YH] &DOFXODU OD SUREDELOLGDG GH TXH XQD SDODEUD QR FRQWHQJD OD OHWUD E &DOFXODU OD SUREDELOLGDG GH TXH XQD SDODEUD WHQJD WRGDV VXV OHWUDV LJXDOHV &DOFXODU OD SUREDELOLGDG GH TXH XQD SDODEUD WHQJD WRGDV VXV OHWUDV GLVWLQWDV &DOFXODU OD SUREDELOLGDG GH TXH XQD SDODEUD WHQJD OD IRUPD ³[FG\´ FXDQGR [ H \ QR SXHGHQ VHU LJXDOHV QL D F QL D G &DOFXODU OD SUREDELOLGDG GH TXH XQD SDODEUD WHQJD OD IRUPD ³[FG\´ (O VXFHVR $ HVWi FRQVWLWXLGR SRU WRGDV ODV SDODEUDV GH OHWUDV TXH QR FRQWLHQHQ OD OHWUD D \ HO VXFHVR % SRU ODV TXH QR FRQWLHQHQ OD OHWUD E &DOFXODU OD SUREDELOLGDG 3$8% (MHUFLFLR (Q XQD XUQD KD\ ERODV EODQFDV \ QHJUDV ¢&XiO HV OD SUREDELOLGDG GH TXH DO H[WUDHU XQD EROD DO D]DU VHD EODQFD" ¢&XiO HV OD SUREDELOLGDG GH TXH QR VHD EODQFD" ¢&XiO HV OD SUREDELOLGDG GH TXH VHD QHJUD" ¢&XiO HV OD SUREDELOLGDG GH TXH VHD URMD" ¢&XiO HV OD SUREDELOLGDG GH TXH VHD EODQFD R QHJUD"

Upload: daniel-sendra-garcia

Post on 06-Sep-2015

3 views

Category:

Documents


0 download

DESCRIPTION

problemas probabilidad

TRANSCRIPT

  • '(3$57$0(172'((67$'67,&$(,2*5$'2(1&,(1&,$6$0%,(17$/(6

    (67$'67,&$

    3UREOHPDV)XQGDPHQWRVGH3UREDELOLGDG(MHUFLFLR &RQVLGHUDQGR HO H[SHULPHQWR GH ODQ]DU XQD PRQHGD HTXLOLEUDGD HVWDEOHFHU HOiOJHEUD GH VXFHVRV IRUPDGD SRU ODV SDUWHV GHO HVSDFLR PXHVWUDO \ FDOFXODU OD SUREDELOLGDG GHREWHQHUFDUDFXDQGRUHDOL]DPRVXQODQ]DPLHQWR(MHUFLFLR6LVHUHDOL]DQODQ]DPLHQWRVGHXQDPRQHGDHTXLOLEUDGD&DOFXODUODVSUREDELOLGDGHVGH

    2EWHQHUXQDFDUD 1RREWHQHUQLQJXQDFDUD 2EWHQHUDOPHQRVXQDFDUD 2EWHQHUFUXFHV

    (MHUFLFLR(QHOODQ]DPLHQWRGHXQGDGRSHUIHFWRWRGDVODVFDUDVWLHQHQODPLVPDSRVLELOLGDGGHVDOLUHQFDGDODQ]DPLHQWR

    &DOFXODUODSUREDELOLGDGGHREWHQHUXQ &DOFXODUODSUREDELOLGDGGHREWHQHUXQRXQ &DOFXODUODSUREDELOLGDGGHREWHQHUXQUHVXOWDGRSDU &DOFXODUODSUREDELOLGDGGHREWHQHUXQPHQRURLJXDOTXH &DOFXODUODSUREDELOLGDGGHREWHQHUXQUHVXOWDGRVXSHULRUD &DOFXODUODSUREDELOLGDGGHREWHQHUXQUHVXOWDGRSDU\QRPD\RUD &DOFXODUODSUREDELOLGDGGHREWHQHUXQUHVXOWDGRSDURLQIHULRURLJXDOD

    6ROXFLRQHV8WLOL]DUHPRVODUHJODGH/DSODFHHQODREWHQFLyQGHORVUHVXOWDGRVGHHVWHHMHUFLFLRGDGRTXHVHWUDWDGHXQH[SHULPHQWRDOHDWRULRFRQXQLYHUVRILQLWR\HOHPHQWRVHTXLSUREDEOHV

    6XFHVR$ REWHQHUXQ ^`3$

    6XFHVR% REWHQHUXQRXQ ^` ^`8^`3% 2EVHUYDUTXHSRGUtDREWHQHUVHXVDQGR3^`3^`

    6XFHVR& REWHQHUXQUHVXOWDGRSDU ^` ^`8^`8^`3&

    6XFHVR' REWHQHUXQUHVXOWDGRPHQRURLJXDOTXH ^`3' 2EVHUYDUTXHSRGUtDREWHQHUVHXVDQGRTXH' %

    6XFHVR( REWHQHUXQUHVXOWDGRPD\RUTXH ^`HVGHFLU( %3( 'HOPLVPRPRGRSRGUtDREWHQHUVHXVDQGRTXH( ' D 3( 3'

    6XFHVR) REWHQHUXQUHVXOWDGRSDU\QRPD\RUD ^`3) 2EVHUYDUTXHHVWHVXFHVRHVODLQWHUVHFFLyQGH&\') &'

    (OVXFHVRREWHQHUXQUHVXOWDGRSDURLQIHULRURLJXDODHVODXQLyQGHORVVXFHVRV&\'&8' ^`3&8' 2EVHUYDUTXHGHODSDUWDGRDQWHULRUWHQHPRVHOVXFHVRLQWHUVHFFLyQGH&\'SRU ORTXHWDPELpQSXHGHREWHQHUVHPHGLDQWHODSURSLHGDG

    3&8' 3&3'3&'

    (MHUFLFLR6HUHDOL]DQODQ]DPLHQWRVGHXQGDGR&DOFXODUODVVLJXLHQWHVSUREDELOLGDGHV /RVUHVXOWDGRVGHORVGRVSULPHURVODQ]DPLHQWRVVHDQ\FRQVHFXWLYDPHQWH /RVUHVXOWDGRVGHORVGRVSULPHURVODQ]DPLHQWRVVHDQ\LQGLVWLQWDPHQWH 2EWHQHUH[DFWDPHQWHXQ\XQHQDOJXQRGHORVODQ]DPLHQWRV (OVXFHVR$HVWiFRQVWLWXLGRSRUWRGRVORVODQ]DPLHQWRVSRVLEOHVHQORVTXHHOUHVXOWDGRHV

    GH OD IRUPD [\ \ HO VXFHVR % SRU WRGRV ORV GH OD IRUPD [\ &DOFXODU ODSUREDELOLGDG3$8%

    6ROXFLRQHV

    2EVHUYDU TXH FDGD UHVXOWDGR GHO H[SHULPHQWR HVWi IRUPDGR SRU FXDWUR FRPSRQHQWHVRUGHQDGDVXQDSRUFDGDODQ]DPLHQWR$VtDOHVSHFLILFDUVyORORVGRVSULPHURVHOVXFHVRSHUPLWHFXDOTXLHUYDORUSRVLEOHSDUDHOWHUFHU\FXDUWRODQ]DPLHQWRHVGHFLU$ ^[\[\FXDOTXLHUYDORUGHOGDGR`

    3[\ FDVRVIDYRUDEOHVFDVRVSRVLEOHV

    3[\8[\ 3[\3[\ SXHVVRQVXFHVRVGLVMXQWRV

    6L TXHUHPRV VyOR XQ \ VyOR XQ HQ HO UHVXOWDGR GH ORV FXDWUR ODQ]DPLHQWRV SULPHURYDPRVDYHUGHFXDQWDVPDQHUDVSRGHPRVFRORFDUHO\HOHQHOUHVXOWDGR3DUDHOORYDPRVDYHUFyPRFRORFDUSULPHURHO\OXHJRFRORFDGRpVWHFRORFDUHO3DUD

    HOKD\VLWLRVFXDOTXLHUDGHORVFXDWURODQ]DPLHQWRV\SDUDHOTXHGDUiQVLWLRVGDQGRXQWRWDO GH SRVLELOLGDGHV &RPR HO SDSHO GHO \ HO VH SXHGHQ LQWHUFDPELDU GDQGR OXJDU DUHVXOWDGRVGLIHUHQWHVHQWRWDOKDEUiUHVXOWDGRVGLIHUHQWHVHQORVTXHKD\XQ\XQ

    (QORVGRVODQ]DPLHQWRVUHVWDQWHVSXHGHREWHQHUVHFXDOTXLHUUHVXOWDGRHQWUHODVFDUDV

    \SRUWDQWRVHUiQHQWRWDO UHVXOWDGRV$VtHQWRWDOWHQGUHPRV[ UHVXOWDGRVIDYRUDEOHV(QWRQFHVODSUREDELOLGDGSHGLGD

    HV3$

    6L $ ^[\ [\ ` \ % ^[\ [\ ` HQWRQFHV $% \ SRUWDQWRODSUREDELOLGDGGHODXQLyQHV

    3$8% 3$3% (MHUFLFLR(OVXFHVRVHJXURHVWiIRUPDGRSRUODVOHWUDVDEFG\H$SDUWLUGHHVWDVVHYDQDIRUPDUDJUXSDPLHQWRVGHOHWUDVFRPREDGDORVTXHGHQRPLQDUHPRVSDODEUDVGHOHWUDV

    &DOFXODUODSUREDELOLGDGGHTXHXQDSDODEUDFRQWHQJDODOHWUDDH[DFWDPHQWHYH] &DOFXODUODSUREDELOLGDGGHTXHXQDSDODEUDFRQWHQJDODOHWUDEDOPHQRVXQDYH] &DOFXODUODSUREDELOLGDGGHTXHXQDSDODEUDQRFRQWHQJDODOHWUDE &DOFXODUODSUREDELOLGDGGHTXHXQDSDODEUDWHQJDWRGDVVXVOHWUDVLJXDOHV &DOFXODUODSUREDELOLGDGGHTXHXQDSDODEUDWHQJDWRGDVVXVOHWUDVGLVWLQWDV &DOFXODUODSUREDELOLGDGGHTXHXQDSDODEUDWHQJDODIRUPD[FG\FXDQGR[H\QRSXHGHQ

    VHULJXDOHVQLDFQLDG &DOFXODUODSUREDELOLGDGGHTXHXQDSDODEUDWHQJDODIRUPD[FG\ (OVXFHVR$HVWiFRQVWLWXLGRSRUWRGDVODVSDODEUDVGHOHWUDVTXHQRFRQWLHQHQODOHWUDD

    \HOVXFHVR%SRUODVTXHQRFRQWLHQHQODOHWUDE&DOFXODUODSUREDELOLGDG3$8%(MHUFLFLR(QXQDXUQDKD\ERODVEODQFDV\QHJUDV

    &XiOHVODSUREDELOLGDGGHTXHDOH[WUDHUXQDERODDOD]DUVHDEODQFD" &XiOHVODSUREDELOLGDGGHTXHQRVHDEODQFD" &XiOHVODSUREDELOLGDGGHTXHVHDQHJUD" &XiOHVODSUREDELOLGDGGHTXHVHDURMD" &XiOHVODSUREDELOLGDGGHTXHVHDEODQFDRQHJUD"

  • (MHUFLFLR(QXQDXUQDKD\ERODVEODQFDV\ERODVQHJUDV'HODPLVPDVHUHDOL]DQH[WUDFFLRQHVcon reem

    plazamiento

    &XiOHVODSUREDELOLGDGGHREWHQHUHOUHVXOWDGREEQ"&XiOHVODSUREDELOLGDGGHREWHQHUFXDOTXLHUUHVXOWDGRGLVWLQWRGHODQWHULRU"&XiOHVODSUREDELOLGDGGHREWHQHUXQRGHORVSRVLEOHVUHVXOWDGRVEE["&XiOHVODSUREDELOLGDGGHREWHQHUERODEODQFDDOPHQRV"&XiOHVODSUREDELOLGDGGHREWHQHUERODVQHJUDVFRPRPi[LPR"&XiOHVODSUREDELOLGDGGHREWHQHUXQUHVXOWDGRGHODIRUPDE[QGRQGH[SXHGHVHUER

    Q"&XiOHVODSUREDELOLGDGGHREWHQHUERODEODQFDFRPRPi[LPR\ERODQHJUDFRPR

    PtQLPR"&DOFXODUODSUREDELOLGDG3$8%VLHQGRORVVXFHVRV$\%

    $ ^EE[[ DRQ`% ^QQ\\ DRQ`(MHUFLFLR(QXQDXUQDKD\ERODVEODQFDV\ERODVQHJUDV'HODPLVPDVHUHDOL]DQH[WUDFFLRQHVsin reem

    plazamiento

    &XiOHVODSUREDELOLGDGGHREWHQHUHOUHVXOWDGRQQE"&XiOHVODSUREDELOLGDGGHREWHQHUFXDOTXLHUUHVXOWDGRGLVWLQWRGHODQWHULRU"&XiOHVODSUREDELOLGDGGHREWHQHUXQRGHORVSRVLEOHVUHVXOWDGRVQQ["&XiOHVODSUREDELOLGDGGHREWHQHUERODEODQFDDOPHQRV"&XiOHVODSUREDELOLGDGGHREWHQHUERODVQHJUDVFRPRPi[LPR"&XiOHVODSUREDELOLGDGGHREWHQHUXQUHVXOWDGRGHODIRUPDE[QGRQGH[SXHGHVHUER

    Q"&XiOHVODSUREDELOLGDGGHREWHQHUERODEODQFDFRPRPi[LPR\ERODQHJUDFRPR

    PtQLPR"&DOFXODUODSUREDELOLGDG3$8%VLHQGRORVVXFHVRV$\%

    $ ^EE[[ DRQ`% ^QQ\\ DRQ`(MHUFLFLR$GLIHUHQFLDGHOGDGRKRQHVWRFRQHOTXHKHPRVWUDEDMDGRHQORVSUREOHPDV\HQHVWHSUREOHPDWUDWDUHPRVFRQXQGDGRWUXFDGRXQGDGRHQHOTXHODVGLVWLQWDVFDUDVWLHQHQGLVWLQWDVSRVLELOLGDGHVGHVDOLUHQFDGDODQ]DPLHQWR8QFDVRGHHVWHWLSRGHGDGRVHVDTXpOHQHOTXHODSUREDELOLGDGGHFDGDFDUDHVSURSRUFLRQDODOQ~PHURGHGLFKDFDUDVL$

    N HVHOVXFHVRREWHQHUODFDUDNHQWRQFHV3$

    N WNGRQGHWHVXQQ~PHURFDUDFWHUtVWLFRGHODIRUPDHQTXHVHKDWUXFDGRHOGDGR

    &DOFXODUHOYDORUGHOQ~PHURW&DOFXODUODSUREDELOLGDGGHGHREWHQHUXQ&DOFXODUODSUREDELOLGDGGHREWHQHUXQRXQ&DOFXODUODSUREDELOLGDGGHREWHQHUXQRXQyXQ&DOFXODUODSUREDELOLGDGGHREWHQHUXQUHVXOWDGRSDU&DOFXODUODSUREDELOLGDGGHREWHQHUXQUHVXOWDGRLPSDU&DOFXODUODSUREDELOLGDGGHQRREWHQHUQLQJXQRGHORVUHVXOWDGRVGHODSDUWDGRDQWHULRU

    (MHUFLFLR3DUDDQDOL]DUODVFRQVHFXHQFLDVTXHWLHQHQGHWHUPLQDGRVKiELWRVGHORVFRQGXFWRUHVHQHOQ~PHURGHPXHUWHVSRUDFFLGHQWHVGHWUiILFRVHKDFRQVLGHUDGRFRPRVXFHVRVHJXURHOIRUPDGRSRUWRGRVORVFRQGXFWRUHV\FRPRVXFHVRVGHHVWXGLRORVVLJXLHQWHV$ ^FRQGXFLUVLQFLQWXUyQ`\% ^FRQGXFLUFRQXQtQGLFHGHDOFRKROHQVDQJUHPD\RUGH`6DELHQGRTXHODVSUREDELOLGDGHVGHORVVXFHVRV$%\$%VRQ3$ 3% \3$% UHVSHFWLYDPHQWHUHVSRQGHUDODVVLJXLHQWHVFXHVWLRQHV

    'LEXMDUHQXQJUiILFRORVVXFHVRV$%$%

    \HOVXFHVRVHJXUR&DOFXODUODVSUREDELOLGDGHV3$

    \3%

    &DOFXODU3$8%4XpFDUDFWHUtVWLFDVWLHQHQORVFRQGXFWRUHVGHOVXFHVR$8%"&DOFXODUODVSUREDELOLGDGHV3$%\3%$&DOFXODU3$8%XWLOL]DQGRORVUHVXOWDGRVGHODSDUWDGRDQWHULRU'LEXMDUHQXQJUiILFRORVVXFHVRV$%%$\$%4XpFDUDFWHUtVWLFDVWLHQHQORVFRQGXFWRUHVGHORVVXFHVRV$%\%$4XpVXFHVRVFRPSRQHQHOiOJHEUDHQJHQGUDGDSRUORVVXFHVRV$\%"

    (MHUFLFLR3DUDDPSOLDUHOFDPSRGHHVWXGLRGHOH[SHULPHQWRDQWHULRUVHKDGHFLGLGRLQFOXLUHOVXFHVR& ^WHQHUyPiVDxRV`$GHPiVGHODVSUREDELOLGDGHVGDGDVRFDOFXODGDVHQVHFRQRFHQODVQXHYDVSUREDELOLGDGHV3& 3$& 3%& \3$%&

    &DOFXODUODVSUREDELOLGDGHV3$8%8&3$8%\3%&

    4XpFDUDFWHUtVWLFDVWLHQHQORVFRQGXFWRUHVTXHHVWiQHQFDGDXQRGHORVVXFHVRV$8 %

    \%& "&DOFXODUODSUREDELOLGDGGH$%8&&DOFXODUODSUREDELOLGDGGH$8%&4XpFDUDFWHUtVWLFDVWLHQHQORVFRQGXFWRUHVTXHHVWiQHQFDGDXQRGHORVVXFHVRVGHORV

    DSDUWDGRV\(MHUFLFLR(QXQDFLXGDGVHFRQVLGHUDTXHHODLUHHVWiHQXQPRPHQWRGDGRFXDQGRORVQLYHOHVGHDPRQtDFRR62

    VXSHUDQGHWHUPLQDGRVOtPLWHV'HQRPLQDUHPRVSRU$\%ORVVXFHVRV$ ^HOQLYHOGHDPRQtDFRVXSHUDVXOtPLWH`\% ^HOQLYHOGH62

    VXSHUDVXOtPLWH6HFRQRFHQODVVLJXLHQWHVSUREDELOLGDGHV3$ 3% \3$%

    &DOFXODUODSUREDELOLGDGGHTXHHODLUHHVWpFRQWDPLQDGR'LEXMDUHQXQJUiILFRHOVXFHVR$8 %

    &DOFXODUODSUREDELOLGDG3$8 %

    4XpFDUDFWHUtVWLFDVWLHQHHODLUHFXDQGRVHUHDOL]DHOVXFHVR$8%

    "'LEXMDUHQXQJUiILFRHOVXFHVR%$&DOFXODUODSUREDELOLGDG3%$4XpFDUDFWHUtVWLFDVWLHQHHODLUHFXDQGRVHUHDOL]DHOVXFHVR%$"&DOFXODUODSUREDELOLGDG3$%3%$4XpLQWHUSUHWDFLyQSXHGHGDUVHDODSUREDELOLGDGDQWHULRU"

    (MHUFLFLR3DUDSURIXQGL]DUHQHOFRQRFLPLHQWRGHODFRQWDPLQDFLyQGHODLUHGHODVFLXGDGHVDORVVXFHVRV$\%GHOSUREOHPDVHKDDJUHJDGRFRPRWHUFHUHOHPHQWRFRQWDPLQDQWHHOTXHHOQLYHOGH&2

    VXSHUHXGHWHUPLQDGROtPLWH$VRFLDGRDHVWHQXHYRIDFWRUVHFRQVLGHUDHOVXFHVR& ^HOQLYHOGH&2

    VXSHUDVXOtPLWH`$GHPiVGHODVSUREDELOLGDGHVGDGDVRFDOFXODGDVGHOSUREOHPDDQWHULRUVHFRQRFHQODVQXHYDVSUREDELOLGDGHV3& 3$& 3%& \3$%&

    &DOFXODUODSUREDELOLGDGGHTXHHODLUHQRHVWpFRQWDPLQDGR&DOFXODUODSUREDELOLGDGGHOVXFHVR$8%&4XpFDUDFWHUtVWLFDVWLHQHHODLUHFXDQGRVHUHDOL]DHOVXFHVR$8%&"&DOFXODUODSUREDELOLGDGGHOVXFHVR$8%&&DOFXODUODSUREDELOLGDGGHOVXFHVR$%8&

    (MHUFLFLR'HGRVVXFHVRV$\%VHFRQRFHQODVVLJXLHQWHVSUREDELOLGDGHV3$ 3% \3$%

    &DOFXODUODSUREDELOLGDG3%$&DOFXODUODSUREDELOLGDGGHOVXFHVR$FRQGLFLRQDGRSRUHOVXFHVR%&DOFXODUODVSUREDELOLGDGHV3$%

    \3%$

    4XpUHODFLRQHVH[LVWHQHQWUHODVSUREDELOLGDGHVFDOFXODGDV"6RQLQGHSHQGLHQWHVORVVXFHVRV$\%"

    6ROXFLRQHV3%$ 3$%3$

    ,JXDOTXHHQHODSDUWDGRDQWHULRU3$% 3$%3%

    (QSHULPHUOXJDUREVHUYDUTXH$VHSXHGHH[SUHVDUFRPRXQLyQGHVXFHVRVGLVMXQWRV

    $ $%8$ \SRUWDQWR3$ 3$3$%$Vt3$ 3$ 3

  • $QiORJDPHQWH3% 3 %3

    3%$3 SRUORTXH%$\ VRQVXFHVRVFRPSOHPHQWDULRV/RPLVPRFRQ$% \ %

    3$% 3$3% SRUORTXHQRVRQLQGHSHQGLHQWHV(MHUFLFLR'RVVXFHVRVLQFRPSDWLEOHV$\%WLHQHQODVSUREDELOLGDGHVUHVSHFWLYDVGH\GHUHDOL]DUVH

    &DOFXODUODVSUREDELOLGDGHVGHORVVXFHVRV$8%\GH$%6RQLQGHSHQGLHQWHV$\%"&DOFXODUODVSUREDELOLGDGHVGHORVVXFHVRV$%

    \%$

    6RQLQGHSHQGLHQWHV$\ %"

    6RQLQGHSHQGLHQWHV%\$"

    6ROXFLRQHV&DOFXODUODVSUREDELOLGDGHVGHORVVXFHVRV$8%\GH$%

    (QSULPHUOXJDUREVHUYDPRVTXHQRVLQGLFDQTXHORVVXFHVRV$\%VRQLQFRPSDWLEOHVHVWRHVTXHQRSXHGHRFXUULUTXHHOUHVXOWDGRGHODH[SHULPHQWDFLyQXREVHUYDFLyQSHUWHQH]FDDDPERVVXFHVRVDODYH]$% \SRUFRQVLJXLHQWH3$% 3

    $SDUWLUGHHVWHYDORUODSUREDELOLGDGGHOVXFHVRXQLyQHVGHFLUGHTXHHOUHVXOWDGRGHOH[SHULPHQWRXREVHUYDFLyQHVWpHQDOJXQRGHORVGRVVXFHVRV$R%HTXLYDOHDTXHHVWHHQDOJXQRGHORVGRV\DTXHHVLPSRVLEOHGHTXHSHUWHQH]FDDDPERVDOPLVPRWLHPSRHVGHFLU

    3$8% 3$3% ORTXHLQGLFDTXHODXQLyQHVHOVXFHVRVHJXURWRGRUHVXOWDGRSRVLEOHHVWiHQDOJXQRGHORVGRVVXFHVRV$R%

    6RQLQGHSHQGLHQWHV$\%"3DUDDQDOL]DUODLQGHSHQGHQFLDGHORVGRVVXFHVRVSRGHPRVXWLOL]DUODGHILQLFLyQGHO

    FRQFHSWRGHLQGHSHQGHQFLDHVGHFLUHOVXFHVR$HVLQGHSHQGLHQWHGHO%VLQRWLHQHUHODFLyQDOJXQDFRQODRFXUUHQFLDGHOPLVPRHVWRHVTXHODSUREDELOLGDGGHRFXUUHQFLDGH$QRVHYHDIHFWDGDSRUTXHKD\DRFXUULGRRQR%3$% 3$3DUDHOORREVHUYDPRVTXH3$ \3$% 3$%3%

    (YLGHQWHPHQWHODSUREDELOLGDGGHRFXUUHQFLDGH$HVWiDIHFWDGDSRUODGH%SRUORTXHQRVRQLQGHSHQGLHQWHVKD\GHSHQGHQFLDHQWUHHOORV

    &DOFXODUODSUREDELOLGDGGHOVXFHVR$%

    3DUDGHWHUPLQDUHVWDSUREDELOLGDGREVHUYDPRVTXH % %WRGRVORVUHVXOWDGRVTXHQR

    HVWiQHQ%$Vt3 % 3% 3$\$\%VRQLQFRPSDWLEOHVSRUORTXH%

    $'HHVWDIRUPD

    3$ % 3$$ 3$$3$

    GDGRTXHXWLOL]DUODLQIRUPDFLyQDSULRULGHTXHHOUHVXOWDGRHVWiHQ$KDFHVHJXURTXHODRFXUUHQFLDGH$HQODH[SHULPHQWDFLyQXREVHUYDFLyQ

    6RQLQGHSHQGLHQWHV$\ %"

    $SDUWLUGHODSDUWDGRDQWHULRUHVFODURTXHQRVRQLQGHSHQGLHQWHV\DTXH% $SRUORTXH

    3$ % 3$

    (QFXDOTXLHUFDVRWDPELpQVHSXHGHREWHQHUSRUHODSDUWDGR\DTXHVLIXHVHQ

    LQGHSHQGLHQWHV$\ %WDPELpQWHQGUtDQTXHVHUOR$\%\\DKHPRVYLVWRHQTXHQRORVRQ

    (MHUFLFLR/DXQLyQGHORVVXFHVRVLQGHSHQGLHQWHV$\%WLHQHXQDSUREDELOLGDG\ODVSUREDELOLGDGHVGHFDGDXQRGHHOORVVRQ\UHVSHFWLYDPHQWH

    &DOFXODUODSUREDELOLGDGGHODLQWHUVHFFLyQGHDPERVVXFHVRV6RQLQFRPSDWLEOHVODVSDUHMDVGHVXFHVRVGHFDGDXQDGHODVSDUHMDV$\%$\%

    $\

    %"6ROXFLRQHV

    3DUDFDOFXODUODSUREDELOLGDGGHODLQWHUVHFFLyQGHDPERVVXFHVRVWHQHPRVTXH3$8% HVODSUREDELOLGDGGHRFXUUHQFLDGHTXHXQUHVXOWDGRHVWpHQDOJXQRGHORVGRVVXFHVRV$R%RHQDPERVDODYH]GDGRTXH

    3$8% 3$3%3$%3RUORTXH

    3$% 3$3%3$8%

    (YLGHQWHPHQWHSRUHODSDUWDGRWHQHPRVTXH$\%QRVRQLQFRPSDWLEOHV\DTXH3$% \VLIXHVHQLQFRPSDWLEOHVHQWRQFHV$% \HOYDFtRWLHQHSUREDELOLGDGQXOD$VLPLVPRSDUDYHUODLQFRPSDWLELOLGDGGH$\%

    WHQHPRVTXHODLQWHUVHFFLyQGHDPERVHVWiGHWHUPLQDGDSRUODRFXUUHQFLDGHXQUHVXOWDGRTXHSHUWHQHFHDDPERVVXFHVRVDODYH]HVGHFLUTXHHVWiHQ$\QRHQ%SRUORTXHSRGtDPRVUHSUHVHQWDUHOWRWDOGH$FRPRODSDUWHGH$TXHWDPELpQHVWiHQ%XQLGDGHIRUPDH[FOX\HQWHDODSDUWHGH$TXHQRHVWiHQ%

    3$ 3$%3$ %

    'HGRQGHVHGHGXFHTXH3$ %

    3$3$%

  • (MHUFLFLR(QXQDXUQDKD\ERODVEODQFDV\ERODVQHJUDV/RVVXFHVRVH[WUDHUERODEODQFD\H[WUDHUERODQHJUDVHGHQRPLQDQ%\1UHVSHFWLYDPHQWH'HGLFKDXUQDVHUHDOL]DQGRVH[WUDFFLRQHVsin reem

    plazamiento

    &DOFXODUODSUREDELOLGDGGHREWHQHUXQDERODQHJUDHQODVHJXQGDH[WUDFFLyQVLHQODSULPHUDVHREWXYRXQDERODEODQFD

    &DOFXODUODSUREDELOLGDGGHREWHQHUXQDERODQHJUDHQODVHJXQGDH[WUDFFLyQ(MHUFLFLR(QXQDXUQDKD\ERODVEODQFDV\ERODVQHJUDV\HQRWUDXUQDKD\ERODVEODQFDV\ERODVQHJUDV/RVVXFHVRVH[WUDHUERODEODQFD\H[WUDHUERODQHJUDVHGHQRPLQDQ%\1UHVSHFWLYDPHQWH6HHOLJHXQDXUQDDOD]DU\GHGLFKDXUQDVHH[WUDHXQDERODDOD]DU

    &DOFXODUODSUREDELOLGDGGHTXHODERODREWHQLGDVHDEODQFD&DOFXODUODSUREDELOLGDGGHTXHODERODREWHQLGDVHDQHJUD6LODERODH[WUDtGDHVEODQFDGHTXpXUQDSURFHGHPiVSUREDEOHPHQWH"

    6ROXFLRQHV6LHQGR8

    \8 ORVVXFHVRVREWHQHUODSULPHUDXUQD\REWHQHUODVHJXQGDXUQD

    UHVSHFWLYDPHQWHODVSUREDELOLGDGHVGHFDGDXQRGHHOORVVRQLJXDOHV38

    38

    /DVSUREDELOLGDGHV3%8 \3%8

    VHREWLHQHQSRUPHGLRGHODUHJODGH/DSODFH3%8

    \3%8 (QWRQFHVXWLOL]DQGRODIyUPXODGHODSUREDELOLGDGWRWDOUHVXOWD

    3% 3%8 38

    3%8 38

    6XVWLWX\HQGRHQHOUD]RQDPLHQWRGHODSDUWDGRDQWHULRU1SRU%REWHQHPRV

    318 \318

    8WLOL]DQGRGHQXHYRODIyUPXODGHODSUREDELOLGDGWRWDOUHVXOWDODSUREDELOLGDG31 318

    38 318

    38

    8WLOL]DUHPRVODIyUPXODGH%D\HVSDUDFDOFXODUODVSUREDELOLGDGHV38

    %\38 %

    UHFXUULHQGRDDOJXQRVGHORVUHVXOWDGRVGHORVDSDUWDGRV\

    P

    BU

    PU

    PU

    BP

    B

    P

    BU

    PU

    PU

    BP

    B

    REWHQLHQGRTXH38 %!38

    %SRUORTXHHVPiVSUREDEOHTXHODERODVHDGHODXUQD(MHUFLFLR 6HGLVSRQHGHXUQDVFRQWHQLHQGRERODVEODQFDV\QHJUDVHQGLVWLQWDSURSRUFLyQ'HQRPLQDQGRSRU8

    8 8

    8 \8

    DHVWDVVXVFRPSRVLFLRQHVUHVSHFWLYDVVRQEQEQEQEQ

    6HHOLJHXQDXUQDDOD]DU\VLQGHWHUPLQDUVXFRPSRVLFLyQVHH[WUDHXQDERODGHODPLVPD/DERODREWHQLGDHVEODQFD&XiOHVODXUQDGHSURFHGHQFLDFRQPi[LPDSUREDELOLGDG"

    6LHOHJLPRVXQDXUQDDOD]DU\GHHVWDH[WUDHPRVXQDERODDOD]DUFXiOHVODSUREDELOLGDGGHOVXFHVR% ^H[WUDHUXQDERODEODQFD`"

    6HHOLJHXQDXUQDDOD]DU\VLQGHWHUPLQDUVXFRPSRVLFLyQVHH[WUDHQFRQUHHPSOD]DPLHQWRGRVERODVGHODPLVPD/DSULPHUDERODREWHQLGDHVEODQFD\ODVHJXQGDQHJUD&XiOHVODXUQDGHSURFHGHQFLDFRQPi[LPDSUREDELOLGDG"

    6LHOHJLPRVXQDXUQDDOD]DU\GHHVWDUHDOL]DPRVGRVH[WUDFFLRQHVDOD]DUFRQUHHPSOD]DPLHQWRFXiOHVODSUREDELOLGDGGHOVXFHVR+ ^ODSULPHUDERODH[WUDtGDHVEODQFD\ODVHJXQGDERODH[WUDtGDHVQHJUD`"

    6RQLQGHSHQGLHQWHVORVVXFHVRV%\+"6HHOLJHXQDXUQDDOD]DU\VLQGHWHUPLQDUVXFRPSRVLFLyQVHH[WUDHQVLQ

    UHHPSOD]DPLHQWRGRVERODVGHODPLVPD/DSULPHUDERODREWHQLGDHVEODQFD\ODVHJXQGDQHJUD&XiOHVODXUQDGHSURFHGHQFLDFRQPi[LPDSUREDELOLGDG"

    (MHUFLFLR6XSRQJDPRVTXHGLVSRQHPRVGHGLVWLQWRQ~PHURGHFDGDXQDGHODVXUQDVGHOSUREOHPDDQWHULRU(QFRQFUHWRGLVSRQHPRVGHXUQDVGHOWLSR8

    GHOWLSR8 GHOWLSR8

    GHOWLSR8

    \GHOWLSR8

    6LHOHJLPRVXQDXUQDDOD]DU\GHHVWDH[WUDHPRVXQDERODDOD]DUFXiOHVODSUREDELOLGDGGHOVXFHVR% ^H[WUDHUXQDERODEODQFD`"

    6LHOHJLPRVXQDXUQDDOD]DU\GHHVWDUHDOL]DPRVGRVH[WUDFFLRQHVDOD]DUFRQUHHPSOD]DPLHQWRFXiOHVODSUREDELOLGDGGHOVXFHVR+ ^ODSULPHUDERODH[WUDtGDHVEODQFD\ODVHJXQGDERODH[WUDtGDHVQHJUD`"

    6RQLQGHSHQGLHQWHVORVVXFHVRV%\+"(MHUFLFLR(QXQDDVLJQDWXUDFXDOTXLHUD;GHGH&LHQFLDV$PELHQWDOHVODFDUJDGRFHQWHGHFDGDDOXPQRHVGHKRUDVVHPDQDOHVHQWUHSUHVHQFLDOHV\QRSUHVHQFLDOHVGHVHiQGRVHFDOFXODUODSUREDELOLGDGGHDSUREDUODDVLJQDWXUDHQIXQFLyQGHOWUDEDMRUHDOL]DGR'HQRPLQDQGRSRU%HOVXFHVRIRUPDGRSRUWRGRVORVDOXPQRVTXHWUDEDMDQRPiVKRUDV\SRU$HOVXFHVRDOXPQRVTXHDSUXHEDQVHFRQRFHQODVVLJXLHQWHVSUREDELOLGDGHV3$ 3% \3$%

    &DOFXODUODSUREDELOLGDGGHTXHDSUXHEHXQDOXPQRTXHWUDEDMDPHQRVGHKRUDVVHPDQDOHV

    &DOFXODUODSUREDELOLGDGGHTXHXQDOXPQRTXHKDVXVSHQGLGRKD\DWUDEDMDGRPiVGHKRUDVVHPDQDOHV

    &DOFXODUTXHSUREDELOLGDGGHDSUREDUWLHQHXQDOXPQRHOHJLGRDOD]DU6RQLQGHSHQGLHQWHVORVVXFHVRV$\%"

    (MHUFLFLR(QUHODFLyQDORVSUREOHPDVVREUHORVDFFLGHQWHVGHWUiILFRHMHUFLFLRV\FRQVLGHUDPRVDKRUDHOVXFHVR0FRQVWLWXLGRSRUWRGRVORVPXHUWRVHQDFFLGHQWHGHWUiILFR6HFRQRFHQORVVLJXLHQWHVGDWRVUHODWLYRVDIDOOHFLPLHQWRV

    xQROOHYDEDQHOFLQWXUyQGHVHJXULGDG

    xH[FHGtDQORVOtPLWHVGHDOFRKROHQVDQJUH

    xWHQtDQPHQRVGHDxRV

    xQROOHYDEDQHOFLQWXUyQGHVHJXULGDG\H[FHGtDQORVOtPLWHVGHDOFRKROHQVDQJUH

    xQROOHYDEDQHOFLQWXUyQGHVHJXULGDG\HUDQPHQRUHVGHDxRV

    xH[FHGtDQORVOtPLWHVGHDOFRKROHQVDQJUH\HUDQPHQRUHVGHDxRV

    xQROOHYDEDQHOFLQWXUyQGHVHJXULGDGH[FHGtDQORVOtPLWHVGHDOFRKROHQVDQJUH\HUDQPHQRUHVGHDxRV

    &DOFXODUODVSUREDELOLGDGHVGHOVXFHVR0HQFDGDXQDGHODVFRQGLFLRQHVHVSHFLILFDGDVPiVDEDMRVREUHODVFDUDFWHUtVWLFDVGHOFRQGXFWRU

    1ROOHYDHOFLQWXUyQGHVHJXULGDG6REUHSDVDORVOtPLWHVGHDOFRKROHQVDQJUH/OHYDHOFLQWXUyQGHVHJXULGDG\WLHQHPHQRVGHDxRV/OHYDHOFLQWXUyQGHVHJXULGDGRWLHQHPHQRVGHDxRV1ROOHYDHOFLQWXUyQGHVHJXULGDGVREUHSDVDORVOtPLWHVGHDOFRKROHQVDQJUH\WLHQHR

    PiVDxRV