práctica 8 teorema de muestreo

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  • 8/15/2019 Práctica 8 Teorema de Muestreo

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    JJEE RRTT JJTT WWTT LL YYLL CCJJTT ÊÊBBEE JJBB LL EE OO BBJJLL EE OO CC WWEE JJDD OO DD YYPP LL NNGGRRJJLL EE OO CC JJEE TT GGPP DD JJRRBBJJYYCCJJEE OO PP JJOO GGEE JJEE FF GGEE JJGGPP ËËOO Z Z TT GGBBEE LL CCLL FF ËËOO RR OO ^̂ OO EE QQOO DD OO RR

    BBll kk wwee jjbboo bbjj ll ee gg rr JJ%% TT gg ll ppëëoo dd gg ccoo rr BB ll kk wwee jjbboo bbjj ll ee gg rr %%

    Y Y p p ïï bbtt jj bboo E E ll %%9988 TT ggll p p ggk k oo dd gg K K wwggrr tt p p ggll

    YYll pp OOc c gg a a o o ee d d p p l l PP o o ññ c c Q Q ggp p ò ò ee H H ggp p ee ï ï ee d d ggq q ss K K o o z z l l ?? : : ## 0 0 9 9 ?? 9 9

    N N W W E E DD O O K K GG E E TT LL RR TT GG ÒÒPP JJ BBLL RR

    Ge clr rjrtgkor oeocòfjblr# cor rgÿocgr rg yplbgroe ge rw tltocjdod% Rje gk`opfl# ge clr rjrtgkor djfjtocgr kldgprg pgqwjgpge ròcl kwgrtpglr dg rgÿocgr yopo yplbgrop% Grtl gr ylrj`cg blkl pgrwctodl dgc tglpgko dgc kwgrtpgl dgrgÿocgr yopo yplbgrop% Grtl gr ylrj`cg blkl pgrwctodl dgc tglpgko dgc kwgrtpgl1

    Weo nwebjòe ygpjòdjbo cjkjtodo ge oebhl dg `oedo bwzo rgpjg dg Nlwpjgp bletjgeg E opkòejbor rg

    grygbjnjbo ñejbokgetg kgdjoetg rwr ~oclpgr 0 E

    - ? jertoetgr ge we ygpjldl%

    Gc kwgrtpgl rg hobg wtjcj oedl we tpge dg ywcrlr l jkywcrlr# lbwyoelrltplr êrtg ñctjkl yopo djbho obbjòe%

    Blerjdêpgrg co rgÿoc bletjewof(t* klrtpodo ge co njfwpo 8%?o*% Êrto ywgdgkwctjycjboprg ylp gc tpge dg jkywcrlr( *qwg rg kwgrtpo ge co njfwpo8%?̀*# dledgT r gr gcjetgp~ocl dg kwgrtpgl dledg gr co npgbwgebjodg kwgrtpgl l co toro dg kwgrtpgl % Co rgÿoc kwgrtpgodo( *gr ylpblerjfwjgetg1 (~êorg njfwpo 8%?b*

    (* (*∟ ( * ∟( * ( * Rw tpoernlpkodo dg Nlwpjgp gr1

    ( * ∟ ( * } ( * { ∟ ( * Ywgdg dgklrtpoprg qwg#

    ∟ ( * ∟ ( * dledg ⁄ % Orë# co tpoernlpkodo dg Nlwpjgp rg ble~jg

    ge1

    ( * ∟ ( * Grtl dgkwgrtpo qwg co tpoernlpkodo dg Nlwpjgp( *dg co rgÿoc dg kwgrtpgl gr weo rwko dg tpoercobjlegr dg

    tpoernlpkodo dg Nlwpjgp dg co rgÿoc lpjfjeoc (`oedo `org*# o weo po òe dg% Yopo orgfwpop co pgbwygpobjòe òytjko

    Njfwpo 8%? o* Rgÿoc Bletjewo (oeocòfjbo*yopo rgp kwgrtpgodo# `* tpge dg jkywcrlr# b* rgÿoc kwgrtpgodo (djfjtoc*%

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    co rgÿoc lpjfjeoc# ¼bwïc dg`g rgp gc jetgp~ocl dg kwgrtpgl< Grto ypgfweto nwedokgetoc ge gc kwgrtpgl rkgdjoetg weo yoptg gqwj~ocgetg dgc tglpgko dg kwgrtpgl%

    Weo npgbwgebjo cjkjtodo ge oebhl dg `oedo# rje blkylegetgr dg npgbwgebjo kozlpgr qwgV hgpt jlr# ywgdgpgbwygpoprg blkycgtokgetg o yoptjp dg kwgrtpor tlkodor ble weo npgbwgebjo oc kgelr dlr ~gbgr rwygpjlp V kwgrtpor ylp rgfwedl% Ge ltpor yoco`por# yopo weo rgÿoc ble okycjtwd dg `oedo dgV hgpt jlr# el hoz yêpdjdo dgjenlpkobjòe l rwygpylrjbjòe# rj co npgbwgebjo dg kwgrtpgl gr oc kgelr gc dl`cg dg co npgbwgebjo kïr octo dg ckldwcobjòe% Ylp cl toetl#

    Grto ñctjko gxypgrjòe rg fgegpo dg co rjfwjgetg koegpo z rwylejgedl qwg 1

    Getlebgr1

    Co npgbwgebjo dg kwgrtpgl rg blelbg blkl npgbwgebjo l po òe dg Ezqwjrt z ⁄ ⁄ grgcjetgp~ocl dg Ezqwjrt% Gr jkylptoetg dgbjp qwg# gc dwoc dgc tglpgko dg kwgrtpgl ge tjgkyl (kwgrtpgl ge npgbwgrto`cgbg qwg co rgÿoc cjkjtodo ge tjgkyl# qwg gr bgpl yopo tldoss # qwgdo dgtgpkjeodo ge nlpko ñejbo ylp corkwgrtpor dg rw grygbtpl dg npgbwgebjor qwg blppgryledge o jetgp~oclr pgfwcopgr kgelpgr o⁄ ]hgpt jlr[% Gr dgbjp1

    ( * ∟ ( *

    DD GG RRO O PP PP LL CC CC LL

    ?%+ Pgblertpwjp co rgÿoc tpjoefwcop dg co Njf% 8%0# wroedl gctglpgko dg kwgrtpgl

    o* wroedl we ygpjldl dgkwgrtpgl %`* Wtjcj op co nòpkwco1

    (* ∟ ( *] ( *[( *

    Rwylejgedl qwg1 ( * ( * Ge we jetgp~ocl1 % Rjgedl z %

    Njfwpo 8%0 Rgÿoc n(t* o kwgrtpgop

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    Rlcwbjòe1

    Ge gc rjfwjgetg bòdjfl dg yplfpokobjòe dgropplccodl ge KOTCO@¥P099:o# dopï rlcwbjòe o ewgrtpl ypl`cgko# blkl rg kgebjleò oc jejbjl dg êrto rgbbjòe dgc pgylptg# pgblertpwjpï co rgÿoc klrtpodo o yoptjp dg kwgrtpor gjetgp~ocl dodl# djbhl kwgrtpgl rg ~gpï ge co fpïnjbor gxywgrtor dwpoetg co gagbwbjòe dg djbhl yplfpoko%

    BÒDJFL GE KOTCO@¥'QGPLE HGPEÏEDGQ OCGAOEDPL POÑC FPWYL1 4@^0'GAGPBJBJL ?bcbdjry(&Ypobtjbo 8% Tglpgko dg kwgrtpgl&*=t;+?91?,?9991?9=nt;(9%0%!t-0*%!( +?93t . t39*-(+9%0%!t-0*%!( 93t . t3?9*- 0%!(t;;9*=njfwpg(?*yclt(t#nt#&p&cjegvjdth*yowrgn;jecjeg(&(9%0%!t-0*%!(+?93t . t39*-(+9%0%!t-0*%!( 93t . t3?9*- 0%!(t;;9*&*=T;jeywt(&Dokg gc ygpjldl dg kwgrtpgl &*nlp e;+?9,T1?1?9,T

    nto;n(T!e*%!((rje((yj,T*%!(t+(T!e****%,((yj,T*%!(t+(T!e****='njfwpg(0*hlcd leyclt(t#nto#&cjegvjdth*

    gedyowrghlcd lnnz;9=nlp e;+?9,T1?1?9,T

    nto;n(T!e*%!((rje((yj,T*%!(t+(T!e****%,(yj%!(t+(T!e****=z;z-nto=

    gedyclt(t#z#&cjegvjdth*yowrg

    Cor fpïnjbor fgegpodor dwpoetg co gagbwbjòe dgc bòdjfl dg yplfpokobjòe nwgple cor rjfwjgetgr% Oc oycjbop co rg pgocj ò we kwgrtpgl ge we jetgp~ocl dg ? rgfwedl# z rg fgegpò co rjfwjgetg fpïnjbo (Njfwpo 8%2*%

    Njfwpo 8%2 Rgÿocgr dg kwgrtpgl ble we jetgp~ocl dg ? rgf%

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    Dgrywêr# rg hobg weo blkyopobjòe dg co rgÿoc lpjfjeoc z rw kwgrtpgl ge gc jetgp~ocl kgebjleodl% L`rgp~g qwg kïxjklr dg cor rgÿocgr kwgrtpor# tlboe co rgÿoc lpjfjeoc (Njfwpo 8%4*%

    Njfwpo 8%4 Blkyopobjòe getpg co rgÿoc lpjfjeoc n(t*z co rgÿoc kwgrtpgodo%

    Ylp ñctjkl# yopo blebcwjp gc kwgrtpgl ge gc borl dg we jetgp~ocl dg ? rgfwedl# rg tlkoe djbhlr ~oclpgr kïxjkl

    pgblertpwzg co fpïnjbo (Njfwpo 8%7*%

    Ohlpo rg oeocj o dg jfwoc koegpo ble we jetgp~ocl dg 9%7 rgfwedlr dg kwgrtpgl%

    Njfwpo 8%> Rgÿoc dg kwgrtpgl ble jetgp~ocl dg 9%7 rgfwedlr

    Njfwpo 8%7 Rgÿoc oyplxjkodo kgdjoetg kwgrtpgl ble we jetgp~ocldg kwgrtpgl dg ? rgfwedl

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    Njfwpo 8%6 Blkyopobjòe getpg co rgÿoc lpjfjeoc z co rgÿoc dg kwgrtpgl

    Njfwpo 8%8 Rgÿoc oyplxjkodo kgdjoetg kwgrtpgl ble we jetgp~ocl dg 9%7 rgfwedlr

    0%+ Pgblertpwjp co rgÿoc tpjoefwcop dg co Njf% 8%:# wroedl gc tglpgko dg kwgrtpgl

    o* wroedl we ygpjldl dgkwgrtpgl %`* Wtjcj op co nòpkwco1

    (* ∟ ( *] ( *[( *

    Rwylejgedl qwg1 ( * ( * Ge we jetgp~ocl1 % Rjgedl z %

    Njfwpo 8%: Rgÿoc n(t*% Oeïcjrjr dg weo rgÿoc tjyl gxylegebjoc

  • 8/15/2019 Práctica 8 Teorema de Muestreo

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    Rlcwbjòe1

    Ge gc rjfwjgetg bòdjfl dg yplfpokobjòe dgropplccodl ge KOTCO@¥P099:o# dopï rlcwbjòe o ewgrtpl ypl`cgko# blkl rg kgebjleò oc jejbjl dg êrto rgbbjòe dgc pgylptg# pgblertpwjpï co rgÿoc klrtpodo o yoptjp dg kwgrtpor gjetgp~ocl dodl# djbhl kwgrtpgl rg ~gpï ge co fpïnjbor gxywgrtor dwpoetg co gagbwbjòe dg djbhl yplfpoko%

    BÒDJFL GE KOTCO@¥'QGPÒE HGPEÏEDGQ OCGAOEDPL POÑC FPWYL1 4@^0'GAGPBJBJL0t;91?,?99917=nt;gxy(+t%,0*='njfwpg(2*yclt(t#nt#&p&cjegvjdth*yowrgn;jecjeg(&gxy(+t%,0*&*=T;jeywt(&Dokg gc ygpjldl dg kwgrtpgl &*nlp e;91?17,T

    nto;n(T!e*%!((rje((yj,T*%!(t+(T!e****%,((yj,T*%!(t+(T!e****=njfwpg(2*

    hlcd leyclt(t#nto#&cjegvjdth*gedyowrghlcd lnnz;9nlp e;91?17,T

    nto;n(T!e*%!((rje((yj,T*%!(t+(T!e****%,(yj%!(t+(T!e****=z;z-nto=

    gedyclt(t#z#&cjegvjdth*

    Rg oeocj opï gc kjrkl borl yopo oyplxjkop l kwgrtpgop co nwebjòe gxylegebjoc klrtpodo ge co njfwpo oetgpjlp

    Yopo ? rgfwedl dg jetgp~ocl dg kwgrtpgl%

    Njfwpo 8%?9 Rgÿoc kwgrtpgodo ge we jetgp~ocl dg kwgrtpgl dg ? rgf%

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    Yopo 9%7 rgfwedlr dg jetgp~ocl dg kwgrtpgl%

    Njfwpo 8%?? Blkyopobjòe getpg co rgÿoc lpjfjeoc z co rgÿoc kwgrtpgodo%

    Njfwpo 8%?0 Pgblertpwbbjòe dg co fpïnjbo o yoptjp dg co rgÿockwgrtpgodo z ble we jetgp~ocl dg kwgrtpgl dg ? rgfwedl%

    Njfwpo 8%?2 Rgÿoc dg kwgrtpgl ble we jetgp~ocl dg 9%7 rgfwedlr

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    Ylp ñctjkl# yopo dop cor l`rgp~objlegr z blkgetopjlr z blebcwjp ble êrtg pgylptg# rg hj l ~lcwetopjokgetg z dgcj`pg we borl gxtpo# yopo gc qwg gc jetgp~ocl dg kwgrtpgl nwgpo dg 9%? rgfwedlr%

    Njfwpo 8%?4 Blkyopobjòe getpg co rgÿoc lpjfjeoc ble rw kwgrtpgl

    Njfwpo 8%?7 Rgÿoc pgblertpwjdo kgdjoetg rw kwgrtpgl ble wejetgp~ocl dg kwgrtpgl dg 9%7 rgfwedlr%

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    Njfwpo 8%?> Rgÿoc dg kwgrtpgl ble we jetgp~ocl dg 9%7

    Njfwpo 8%?6 Rgÿoc pgblertpwjdo o yoptjp dg rw kwgrtpgl wtjcjqoedl we jetgp~ocl dg 9%? rgfwedlr%

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    LL @@RRGG PP ^ ^ O O BBJJ LL E E GG RR Z Z BBLL K K GG E E TT O O PP JJ LL RR

    Ge cor fpïnjbor klrtpodor ge gc dgropplccl dg êrtg pgylptg# rg hj l eltop qwg ge co oycjbobjòe dgc tglpgko dgrg l`tjgeg weo kgalp oyplxjkobjòe ble jetgp~oclr kïr ygqwgÿlr dg tjgkyl dg kwgrtpgl= grtl rg ~g ge cor ñctjkor dfpïnjbor# ge dledg oc dop we jetgp~ocl ygqwgÿl dg kwgrtpgl# rg ywgdg oyplxjkop ble kozlp ypgbjrjòe o co rgÿkwgrtpgo# z kgdjoetg djbhor kwgrtpor# rg pgblertpwzò co rgÿoc lpjfjeoc ble kwbho kozlp oyplxjkobjòe o djbhorcjkjtodor ge `oedo%

    Ygpl rj `jge rg ro`g# ge rgetjdl pjfwplrl# cor rgÿocgr cjkjtodor ge `oedo el gxjrtge ygpl ge co ypïbtjbo co kozlpcor rgÿocgr rg ywgdge blerjdgpop blkl oyplxjkodokgetg cjkjtodor ge `oedo dg`jdl o qwg co kozlp yoptg dg co gegrtï bletgejdo horto bjgptl ~oclp njejtl dg npgbwgebjo ge rw grygbtpl% Dg grto koegpo# gc gpplp qwg rg blkgtg oblkylegetgr dg kozlp npgbwgebjo pgrwcto dgrypgbjo`cg%

    BBLL E E BBCC W W RRJJ LL E E GG RR

    Ge co kldgpeo tglpëo dg co blkwejbobjòe# gc tglpgko dg kwgrtpgl blertjtwzg we ypjebjyjl kwz jkylptoetg# yw`org ge êc rg ywgdge ble~gptjp cor rgÿocgr bletjewor ge rgÿocgr djrbpgtor% Grto ble~gprjòe pgypgrgeto ~getoao ywgr ygpkjtg gc koegal dg we eñkgpl njejtl dg ~oclpgr dg co rgÿoc ge cwfop dg we eñkgpl jenjejtl dg ~oclpgr qwco rgÿoc bletjewo% Blkl cl dgkwgrtpo gc tglpgko# grtg eñkgpl njejtl dg ~oclpgr grtï blertjtwjdl ylp co rgbwgebjo dg cor kwgrtpor dg co rgÿoc qwg bletjgege tldo co jenlpkobjòe dg n(t*%Ge blebcwrjòe# tldl gc bletgejdl dg jenlpkobjòe dgco rgÿoc bletjewo cjkjtodo ge `oedo rg ywgdg pggkyco op ylp kwgrtpor dg co rgÿoc rje pjgrfl dg ygpdgp gc

    jenlpkobjòe% @oal grtor bledjbjlegr# gc ypl`cgko dg tpoerkjtjp rgÿoc bletjewo rg pgdwbg oc dg tpoerkjtjp we eñkdg ~oclpgr% Co rgÿoc qwg kïr ble~jgeg yopo co tpoerkjrjòe g grtlr ~oclpgr gr co rgÿoc ywcrl pgbtoefwcop (tpgbwzlr yopïkgtplr rg ywgdge wtjcj op yopo tpoerkjtjp ge nlpko kldwcodo co jenlpkobjòe djrbpgto%

    PP GG N N GG PP GG E E BBJJ O O RR

    ]?[ OCGXOEDGP# BHOPCGR . RODJMW# KOTHGV E%L%= – Nwedokgetlr dg Bjpbwjtlr Gcêbtpjblr ‛# 2po% Gd%#KbFpovHjcc# Kêxjbl# 0996% Boyëtwcl ?8 Tpoernlpkodo dg Nlwpjgp# yïfr% Blerwctodor% 828 o 849%

    ]0[ HGPPGPO YÊPGQ# GEPJ_WG# –Blkwejbobjlegr J1 Rgÿocgr# Kldwcobjòe z Tpoerkjrjòe ‛# ?po% Gd%# Cjkwro#Kêxjbl# 0998% Boyëtwcl JJJ1 Ble~lcwbjòe z Kwgrtpgl# yïfjeor blerwctodor ??> o ?07%