(ebook - pdf)[ingenieria][matematicas] edicions upc - estadistica aplicada per a enginyeria - cata

(ebook - pdf)[ingenieria][matematicas] edicions upc - estadistica aplicada per a enginyeria - cata

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Unformatted text preview: Estadística aplicada per a enginyeria Antoni Ras Sabidó EDICIONS UPC Primera edició: juny de 1993 Reimpressió: setembre de 1994 En col⋅laboració amb el Servei de Llengües i Terminologia de la UPC. Disseny de la coberta: © © Antoni Gutiérrez Antoni Ras Sabidó, 1993 Edicions UPC, 1993 Edicions de la Universitat Politècnica de Catalunya, SL Jordi Girona Salgado 31, 08034 Barcelona Tel. 93 401 68 83 Fax 93 401 58 85 Edicions Virtuals: www.edicionsupc.es e-mail: [email protected] Producció: Servei de Publicacions de la UPC i CPDA (Centre de Publicacions d'Abast) Av. Diagonal 647, ETSEIB, 08028 Barcelona Dipòsit legal: B-20.056-93 ISBN: 84-7653-284-9 Són rigorosament prohibides, sense l'autorització escrita dels titulars del copyright, sota les sancions establertes a la llei, la reproducció total o parcial d'aquesta obra per qualsevol procediment, inclosos la reprografia i el tractament informàtic, i la distribució d'exemplars mitjançant lloguer o préstec públics. 3 U HVHQ WDFLw R  3 U HVHQWDFLw R $TXHVW OOLEUH Ww O RULJHQ HQ XQD SXEOLFDFLw DQRPHQDGD $SXQWV G HVWDGw H R tVWLFD TXH SUHWHQLD VHUYLU GH VXSRUW D OD GRFvQFLD G DTXHVWD PDWvULD LQFORVD HQ HOV YHOOV SODQV G HVWXGLV G (QJLQ\HULD H H 7vFQLFD ,QGXVWULDO FRP D SDUW GH O DVVLJQDWXUD G $PSOLDFLw GH 0DWHPvWLTXHV D O (VFROD 8QL H R D YHUVLWvULD 3ROLWvFQLFD GH 9LODQRYD L OD *HOWUw $O VHX WRUQ DTXHVWV DSXQWV HVWDYHQ LQVSLUDWV D H X HQ XQD FROc OHFFLw GH WH[WRV GH UHIHUvQFLD SXEOLFDWV SHO 'HSDUWDPHQW G (VWDGwVWLFD L ,QYHVWLJDFLw R H t R 2SHUDWLYD HQ HO FRQWH[W GH OHV DVVLJQDWXUHV GH O vUHD TXH V LPSDUWHL[HQ DO U FXUV G (QJLQ\HULD D 6XSHULRU ,QGXVWULDO D OD (76(,% $L[v LPSOLFDYD EvVLFDPHQW GXHV FRVHV TXH O RULHQWDFLw GHO R D R PDWHULDO HUD FDS D O (VWDGwVWLFD $SOLFDGD SDUWLFXODUPHQW DO &RQWURO GH 4XDOLWDW L TXH DTXHVW t PDWHULDO YROLD RIHULU PwV DYLDW XQ VHJXLW GH UHVXPV H[HPSOHV L LOc OXVWUDFLRQV PwV TXH QR XQ H H WUDFWDW WHvULF FOvVVLF L FRPSOHW VREUH OD PDWvULD R D H 3HU D OD FRQYHUVLw HQ OOLEUH KHP PDQWLQJXW O RULHQWDFLw SHO TXH ID DOV FRQWLQJXWV $L[w SHU R R t H[HPSOH HV FRPHQ|D SHO WUDFWDPHQW GH GDGHV L QR SDV SHU OD WHRULD GH SUREDELOLWDWV OD TXDO HV F UHGXHL[ D OD PwQLPD H[SUHVVLw FRQVLGHUDQWOD DTXw VLPSOHPHQW FRP XQ FRL[w WHvULF QHFHVVDUL t R t tR SHU IRQDPHQWDU OHV GLIHUHQWV WvFQLTXHV HVWDGwVWLTXHV TXH HV SUHVHQWHQ PwV HQGDYDQW (Q FDQYL H t H SHO TXH ID DO VHX FDUvFWHU KHP DPSOLDW OD SDUW H[SOLFDWLYD GH PDQHUD TXH SXJXL VHUYLU XQ [LF D PwV FRP D OOLEUH GH WH[W L QR WDQ VROV FRP D FRPSHQGL GH GHpQLFLRQV L TXDGUHV VLQv H RSWLFV R FRO OHFFLw GH SUREOHPHV LOc OXVWUDWV (Q TXDOVHYRO FDV HO GHVHQYROXSDPHQW WHvULF QR wV JHQV H[KDXVWLX R R H L VRYLQW VREUHWRW HQ SDUODU GH OD WHRULD GH SUREDELOLWDWV V RPHWHQ OHV GHPRVWUDFLRQV 7RW L DL[v KHP LQWHQWDW GHIXJLU O HVWLO GH ?UHFHSWDUL GH PvWRGHV SUvFWLFV SHUTXv SHQVHP TXH SHU R H D H WDO G DSOLFDU FRUUHFWDPHQW XQD UHFHSWD L G LQWHUSUHWDU Ew HOV UHVXOWDWV FDO WHQLU XQD QRFLw FODUD H R G DOOv TXH HV ID L GH SHU TXv HV ID G DTXHOOD L QR G XQD DOWUD PDQHUD R H (OV WHPHV G (VWDGwVWLFD TXH WUDFWHP VwQ OD GHVFULSWLYD OD LQIHUvQFLD HO FRQWURO GH TXDOLWDW L OD t R H UHJUHVVLw 3HU WDQW PDQTXHQ DOJXQV WvSLFV FOvVVLFV FRP SHU H[HPSOH O DQvOLVL GH OD YDULvQFLD R R D D D R HO GLVVHQ\ H[SHULPHQWDO /D WULD V KD IHW SHQVDQW HQ XQ FXUV G HVWDGw tVWLFD GLULJLW EvVLFDPHQW D D HVWXGLDQWV G HQJLQ\HULD WvFQLFD L V DGDSWDULD Ew FUHLHP D XQD DVVLJQDWXUD G XQV VLV FUvGLWV H H H FRP VRO DSDUvL[HU HQ IRU|D SODQV G HVWXGLV VHPSUH L TXDQ HQ LPSDUWLU DTXHVWD DVVLJQDWXUD HV H F GRQL XQ SHV LPSRUWDQW D OD SDUW SUvFWLFD L HV GLVSRVL G DOJXQD PHQD GH VXSRUW LQIRUPvWLF FRP D D DUD 6W DW JU DSKLF V 0 LQLW DE  /DVW EXW QRW OHDVW YROGULD H[SUHVVDU HO PHX DJUD…PHQW D DOJXQHV GH OHV SHUVRQHV VHQVH O DMXW GH t OHV TXDOV PDL SRGULD KDYHU SHQVDW D HVFULXUH DTXHVW WH[W DO 'U $OEHUW 3UDW TXH HP YD RULHQWDU © Els autors, 1998; © Edicions UPC, 1998.  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( VWDG w tVWLFD DS OLFDG D S HU D HQ JLQ \ HU LD  ,QWHUYDOV GH FRQpDQ|D F 8Q FRS KHP WULDW HVWLPDGRUV GHOV SDUvPHWUHV TXH HQV LQWHUHVVHQ L FRQHL[HP OHV GLVWULEXFLRQV D TXH VH OV DVVRFLD SRGHP FRPHQ|DU D RFXSDUQRV GH OD SUHFLVLw GHV GHO SXQW GH YLVWD GH OD F R SUREDELOLWDW GH O DSUR[LPDFLw TXH KHP IHW 8QD SULPHUD PDQHUD G DWDFDU OD T… R wV DPE HOV R XHVWLw H LQWHUYDOV GH FRQpDQ|D  /D LGHD wV OD VHJ…HQW KHP FDOFXODW HO YDORU DSUR[LPDW G XQ SDUvPHWUH } F H X D TXH QR FRQHL[HP HVFULXUHP } SHU LQGLFDU TXH HQV SRGHP UHIHULU D z  z; z< R ; <  SHU PLWMv G XQ HVWLPDGRU G DTXHVW SDUvPHWUH L DUD YROGUHP WUREDU XQ LQWHUYDO FRQVWUX… D SDUWLU D D tW GH O HVWLPDGRU GLQV HO TXDO SXJXHP JDUDQWLU DPE XQD SUREDELOLWDW Pw tQLPD SUHp[DGD TXH HV WURED HO YDORU FRUUHFWH GHO SDUvPHWUH ' DTXHVWD SUREDELOLWDW VH Q GLX HO QLYHOO GH FRQpDQ|D L D F O LQGLFDUHP SHU  o b b (Q SULPHU OORF YHXUHP FRP HV FRQVWUXHL[ XQ LQWHUYDO SHU D z TXDQ WDPSRF FRQHL[HP OD YDULvQFLD  &RP KHP GLW HQV EDVDUHP HQ ; SHU IHUKR $WvV TXH OD PLWMDQD PRVWUDO Ww XQD D H H GLVWULEXFLw VLPvWULFD KL KD OD PDWHL[D SUREDELOLWDW TXH HO YDORU FRUUHFWH GH z VLJXL PwV JUDQ R H H R PwV SHWLW TXH OD [ GH OD QRVWUD PRVWUD UHFRUGHX TXH ; z wV XQD QRUPDO DPE HVSHUDQ|D H H F   3HU WDQW wV OvJLF TXH HO QRVWUH LQWHUYDO HVWLJXL FHQWUDW HQ HO YDORU GH OD PLWMDQD PRVWUDO L HR VLJXL VLPvWULF UHVSHFWH G DTXHVW QRPEUH HV D GLU TXH VLJXL GH OD IRUPD >[ %o  [  %o @  (QV H w H TXHGD FRQFUHWDU TXDQW KD GH YDOGUH %o  $UD Ew b b  b o 3 b ; )WQ> v b x Sw Sx S b xx v vb w v w w S b  S   S b  %o z ; %o c 3 vb 6 %o ; 6 z %o Q Q 6 Q %o 6 )WQ>  %o 6 S w Q )WQ> %o 6 Q )WQ> %o 6 Q Q  b o  H +HP XWLOLW]DW TXH OD GLVWULEXFLw GH UHIHUvQFLD SHU D ; z 6 Q wV XQD W DPE Q  JUDXV R H GH OOLEHUWDW L TXH DTXHVWD YDULDEOH Ww IXQFLw GH GHQVLWDW VLPvWULFD  (Q FRQFOXVLw SHU FRQVWUXLU H R H R O LQWHUYDO XQ FRS p[DW HO QLYHOO GH FRQpDQ|D  o KHP GH FHUFDU TXLQ wV HO QRPEUH SHU DO TXDO F H O vUHD D O HVTXHUUD HQ OD JUvpFD GH GHQVLWDW G XQD WQ> YDO  o   GHVSUwV PXOWLSOLTXHP D D H DTXHVW QRPEUH SHO YDORU TXH KD SUHV 6 HQ OD QRVWUD PRVWUD KR GLYLGLP SHU O DUUHO TXDGUDGD GHO QRPEUH G HOHPHQWV GH OD PRVWUD L DL[w REWHQLP OD TXDQWLWDW %o TXH FDO VXPDU L UHVWDU D OD t PLWMDQD GH OD PRVWUD SHU GHWHUPLQDU FRPSOHWDPHQW O LQWHUYDO b b S b b /D WvFQLFD SHU IHU OD UHVWD G LQWHUYDOV HV GHGXHL[ GH PDQHUD DQvORJD $TXw WHQLX XQ TXDGUH RQ H D t HV UHVXPHL[ OD IRUPD GH FDOFXODUORV © Els autors, 1998; © Edicions UPC, 1998. & DS w  3 U RE DE LOLWDW L LQ IHU vQ FLD tWRO H  3DUvPHWUH D z ,QWHUYDO >[ >[  FRQHJXGD z b b x $o  [  $o @  %o @  v )1  &vOFXO D $o  S w v )WQ> Q    GHVFRQHJXGD  %o  [  %o V Q S w &o b o o  V   V y e )W &o 'o    )ƒ )ƒ  >  Q Q Q >  Q b b z; ;  b b   z< < d G  b b b b (o  G [ G b b   (o \ c Q; Q< >   % %U # H V b  c b  c 'o (o b  o b o  Q;   Q<  & & $   b o z; z< < d G *o  G [  *o \ ;   G c e ) Wx  % % %V % # Q; > Q; > *o V; Q;   V< Q<   & & & & $  b o ;  < x  V;  V<  +o  V; V<  y -o  !  !  )) Q< >  +o Q< >  -o  )) o b o   3URYHV G KLSvWHVLV R 8Q DOWUH XV GH O LQIHUvQFLD HVWDGwVWLFD HVWv GHWHUPLQDW SHU OHV DQRPHQDGHV SURYHV ^R WHVWV^ w H t D G KLSvWHVLV  $UD HV WUDFWDUv GH GHFLGLU D SDUWLU GHOV YDORUV PRVWUDOV VL SRGHP DFFHSWDU R QR R D D SDUWLU GH FRQGLFLRQV SUREDELOwVWLTXHV TXH HO SDUvPHWUH TXH GHVFRQHL[HP Ww XQ FHUW YDORU t D H GRQDW /D IRUPXODFLw H[DFWD wV OD VHJ…HQW SHU DO SDUvPHWUH } FRQIURQWDUHP OD KLSvWHVL R H X D R QXO OD + DOOv TXH YROHP FRPSURYDU  TXH VHUv GHO WLSXV +  } R D }  HQIURQW G XQD D KLSvWHVL DOWHUQDWLYD + TXH KDXUHP GH SURSRVDU HQ FDGD FDV  (O UHVXOWDW GHO WHVW HQV GLUv R TXLQD GH OHV GXHV KLSvWHVLV wV PwV FUH…EOH GHV G XQ SXQW GH YLVWD HVWDGwVWLF 3HU UHVSRQGUH R H H t t KR HV FRQVWUXHL[ WRW VXSRVDQW TXH + wV FHUWD XQD GLVWULEXFLw GH UHIHUvQFLD = SHU D H R H O HVWLPDGRU GH } $ SDUWLU G DTXHVWD GLVWULEXFLw HV FRQVWUXHL[ XQD UHJLw G DFFHSWDFLw  TXH R R R DJUXSL DTXHOOV YDORUV TXH ?UDRQDEOHPHQW KRP SRW HVSHUDU TXH V HVGHYLQJXLQ SHU D XQD YDULDEOH DPE WDO GLVWULEXFLw $OHVKRUHV VL HO YDORU ] TXH KD SUHV OD YDULDEOH = HQ OD QRVWUD PRVWUD FDX R c © Els autors, 1998; © Edicions UPC, 1998.  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This note was uploaded on 01/04/2011 for the course MATH 123 taught by Professor Pepe during the Spring '10 term at Universidad Politécnica de Cartagena.

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