121 Pages

# sol.exam2.02

Course Number: STAT 581, Fall 2008

College/University: Washington

Word Count: 61772

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Coursehero >> Washington >> Washington >> STAT 581

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Fi(\022)2864 1496 y Ff(2)2903 1537 y Fi(=)p Fk(8$$)28 b(=)f(exp)q($$)p Fh(\000)p Fi(\022)3482 1496 y Ff(2)3522 1537 y Fi(=)p Fk(8$$)17 b Fi(:)304 1744 y Fk(Hence)1070 1950 y Fi(H)1159 1909 y Ff(2)1198 1950 y Fk($$)p Fi(P)s(;)g(Q)p Fk($$)27 b(=)h(1)21 b Fh(\000)i Fi(\032)p Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)28 b(=)f(1)22 b Fh(\000)h Fk(exp)q($$)p Fh(\000)p Fi(\022)2689 1909 y Ff(2)2729 1950 y Fi(=)p Fk(8$$)17 b Fi(:)304 2156 y Fk($$c$$)33 b(W)-8 b(e)33 b(compute)f Fi(\021)t Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)32 b(\014rst.)44 b(Since)33 b Fi(\036)p Fk($$)p Fi(x)p Fk($$)27 b Fh(\025)h Fi(\036)p Fk($$)p Fi(x)23 b Fh(\000)f Fi(\022)s Fk($$)33 b(if)e(and)i(only)f(if)1290 2340 y(1)p 1219 2384 191 4 v 1219 2404 a Fh(p)p 1302 2404 108 4 v 83 x Fk(2)p Fi(\031)1419 2407 y(e)1464 2366 y Fd(\000)p Fg(x)1559 2343 y Fb(2)1594 2366 y Fg(=)p Ff(2)1696 2407 y Fh(\025)1882 2340 y Fk(1)p 1811 2384 191 4 v 1811 2404 a Fh(p)p 1894 2404 108 4 v 83 x Fk(2)p Fi(\031)2029 2407 y Fk(exp)q($$)p Fh(\000)p Fk(\()p 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y Fg(\022)r(=)p Ff(2)2740 3609 y Fi(\036)p Fk($$)p Fi(x)p Fk($$)p Fi(dx)1579 3908 y Fk(=)1738 3772 y Fc(Z)1838 3799 y Fd(\000)p Fg(\022)r(=)p Ff(2)1793 3998 y Fd(\0001)2019 3908 y Fi(\036)p Fk($$)p Fi(y)t Fk($$)p Fi(dy)h Fk(+)f(1)g Fh(\000)h Fk(\010$$)p Fi(\022)s(=)p Fk(2$$)1579 4113 y(=)83 b(\010$$)p Fh(\000)p Fi(\022)s(=)p Fk(2$$)23 b(+)f(1)f Fh(\000)i Fk(\010$$)p Fi(\022)s(=)p Fk(2$$)17 b Fi(;)212 b Fk(if)63 b Fi(\022)31 b(>)d Fk(0)17 b Fi(:)304 4319 y Fk(When)33 b Fi(\022)e(<)d Fk(0,)k Fi(\022)s(x)23 b Fh(\000)g Fi(\022)1150 4283 y Ff(2)1189 4319 y Fi(=)p Fk(2)k Fi(<)h Fk(0)k(if)g(and)g(only)g(if)g Fi(x)c Fh(\025)g Fi(\022)s(=)p Fk(2,)k(and)h(this)f(yields)805 4462 y Fc(Z)921 4598 y Fi(p)p Fk($$)p Fi(x)p Fk($$)22 b Fh(^)h Fi(q)t Fk($$)p Fi(x)p Fk($$)p Fi(dx)83 b Fk(=)1738 4462 y Fc(Z)1838 4488 y Fd(1)1793 4688 y Fg(\022)r(=)p Ff(2)1929 4598 y Fi(\036)p Fk($$)p Fi(x)22 b Fh(\000)h Fi(\022)s Fk($$)p Fi(dx)f Fk(+)2514 4462 y Fc(Z)2614 4488 y Fg(\022)r(=)p Ff(2)2569 4688 y Fd(\0001)2740 4598 y Fi(\036)p Fk($$)p Fi(x)p Fk($$)p Fi(dx)1579 4812 y Fk(=)83 b(\010$$)p Fi(\022)s(=)p Fk(2$$)22 b(+)g(1)g Fh(\000)h Fk(\010$$)p Fh(\000)p Fi(\022)s(=)p Fk(2$$)17 b Fi(;)212 b Fk(if)63 b Fi(\022)31 b(>)d Fk(0)17 b Fi(:)304 5018 y Fk(It)33 b(follo)m(ws)e(that)736 5258 y Fi(d)787 5273 y Fg(T)10 b(V)899 5258 y Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)27 b(=)h(1)21 b Fh(\000)i Fi(\021)t Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)27 b(=)1908 5118 y Fc(\032)2025 5197 y Fk(\010$$)p Fi(\022)s(=)p Fk(2$$)22 b Fh(\000)g Fk(\010$$)p Fh(\000)p Fi(\022)s(=)p Fk(2$$)p Fi(;)84 b(\022)31 b(>)c Fk(0)2025 5317 y(\010$$)p Fh(\000)p Fi(\022)s(=)p Fk(2$$)22 b Fh(\000)h Fk(\010$$)p Fi(\022)s(=)p Fk(2$$)p Fi(;)83 b(\022)31 b(<)c Fk(0)17 b Fi(:)304 5527 y Fk(The)36 b(follo)m(wing)c(Figure)i (sho)m(ws)i Fi(K)7 b Fk($$)p Fi(P)1704 5542 y Ff(0)1743 5527 y Fi(;)17 b(P)1850 5542 y Fg(\022)1889 5527 y Fk($$,)35 b Fi(H)2078 5491 y Ff(2)2117 5527 y Fk($$)p Fi(P)2218 5542 y Ff(0)2258 5527 y Fi(;)17 b(P)2365 5542 y 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All Rights Reserved. systemdict /setpacking known { currentpacking true setpacking } if userdict /Adobe_AGM_Core 233 dict dup begin put /nd{ null def }bind def /Adobe_AGM_Core_Id /Adobe_AGM_Core_2.0_0 def /AGMCORE_str256 256 string def /AGMCORE_src256 256 string def /AGMCORE_dst64 64 string def /AGMCORE_srcLen nd /AGMCORE_save nd /AGMCORE_graphicsave nd /AGMCORE_imagestring0 nd /AGMCORE_imagestring1 nd /AGMCORE_imagestring2 nd /AGMCORE_imagestring3 nd /AGMCORE_imagestring4 nd /AGMCORE_imagestring5 nd /AGMCORE_c 0 def /AGMCORE_m 0 def /AGMCORE_y 0 def /AGMCORE_k 0 def /AGMCORE_mbuf () def /AGMCORE_ybuf () def /AGMCORE_kbuf () def /AGMCORE_gbuf () def /AGMCORE_bbuf () def /AGMCORE_cmykbuf 4 array def /AGMCORE_screen [currentscreen] cvx def /AGMCORE_tmp 0 def /AGMCORE_arg1 nd /AGMCORE_arg2 nd /AGMCORE_&setgray nd /AGMCORE_&image nd /AGMCORE_&colorimage nd /AGMCORE_&imagemask nd /AGMCORE_&setcolor nd /AGMCORE_&setcolorspace nd /AGMCORE_&&setcolorspace nd /AGMCORE_cyan_plate nd /AGMCORE_magenta_plate nd /AGMCORE_yellow_plate nd /AGMCORE_black_plate nd /AGMCORE_plate_ndx nd /AGMCORE_get_ink_data nd /AGMCORE_is_cmyk_sep nd /AGMCORE_in_rip_sep nd /AGMCORE_host_sep nd /AGMCORE_will_host_sep nd /AGMCORE_avoid_L2_sep_space nd /AGMCORE_composite_job nd /AGMCORE_producing_seps nd /AGMCORE_ccimage_exists nd /AGMCORE_ps_level -1 def /AGMCORE_ps_version -1 def /AGMCORE_environ_ok nd /AGMCORE_CSA_cache 0 dict def /AGMCORE_CSD_cache 0 dict def /AGMCORE_pattern_cache 0 dict def /AGMCORE_currentoverprint false def /AGMCORE_deltaX nd /AGMCORE_deltaY nd /AGMCORE_name nd /AGMCORE_sep_special nd /AGMCORE_ndx nd /AGMCORE_err_strings nd /AGMCORE_cur_err nd /AGMCORE_ovp nd /AGMCORE_CRD_cache where{ pop }{ /AGMCORE_CRD_cache 0 dict def }ifelse /bdf { bind def } bind def /xdf { exch def } def /ldf { load def } def /ddf { put } def /xddf { 3 -1 roll put } def /xpt { exch put } def /bdict { mark } def /edict { counttomark 2 idiv dup dict begin {def} repeat pop currentdict end }def /ps_level /languagelevel where{ pop languagelevel }{ 1 }ifelse def /level2 ps_level 2 ge def /level3 ps_level 3 ge def /ps_version {version cvr} stopped { -1 def /ndf { }if } def /skip_image { has_color ne{ dup 256 idiv {currentfile AGMCORE_str256 readstring pop pop}repeat currentfile AGMCORE_str256 0 4 -1 roll 256 mod getinterval readstring pop pop }{ pop }ifelse } def /addprocs { 2{/exec load}repeat 3 1 roll [ 5 1 roll ] bind cvx } def /colorbuf { 0 1 2 index length 1 sub { dup 2 index exch get 255 exch sub 2 index 3 1 roll put } for } def /makereadonlyarray { /packedarray where {pop packedarray} {array astore readonly} ifelse } def /getspotfunction { AGMCORE_screen exch pop exch pop dup type /dicttype eq { dup /HalftoneType get 1 eq { /SpotFunction get } { dup /HalftoneType get 2 eq { 1 index where{ pop pop pop }{ dup xcheck {bind}if def }ifelse mul add 1 sub} /GraySpotFunction get } { pop {abs exch abs 2 copy add 1 gt {1 sub dup mul exch 1 sub dup } def /clp_npth { clip newpath } def /eoclp_npth { eoclip newpath } def /stkpath_clp_npth { strokepath clip newpath } def /stk_n_clp_npth { gsave stroke grestore clip newpath } def /npth_clp { newpath clip } def /graphic_setup { /AGMCORE_graphicsave save def concat 0 setgray 0 setlinecap 0 setlinejoin 1 setlinewidth [] 0 setdash 10 setmiterlimit newpath false setoverprint false setstrokeadjust userdict begin /showpage {} def mark } def /graphic_cleanup { cleartomark end AGMCORE_graphicsave restore } def /compose_error_msg { } if {dup mul exch dup mul add 1 exch sub}ifelse}bind } ifelse } ifelse grestoreall initgraphics /Helvetica findfont 10 scalefont setfont /AGMCORE_deltaY 100 def /AGMCORE_deltaX 310 def /AGMCORE_arg2 xdf /AGMCORE_arg1 xdf clippath pathbbox newpath pop pop 36 add exch 36 add exch moveto 0 AGMCORE_deltaY rlineto AGMCORE_deltaX 0 rlineto 0 AGMCORE_deltaY neg rlineto AGMCORE_deltaX neg 0 rlineto closepath 0 AGMCORE_&setgray gsave 1 AGMCORE_&setgray fill grestore 1 setlinewidth gsave stroke grestore currentpoint AGMCORE_deltaY 15 sub add exch 8 add exch moveto /AGMCORE_deltaY 12 def /AGMCORE_tmp 0 def AGMCORE_err_strings exch get { dup 32 eq { pop AGMCORE_str256 0 AGMCORE_tmp getinterval dup (.) ne AGMCORE_arg1 0 lt and { pop } { stringwidth pop currentpoint pop add AGMCORE_deltaX 28 add gt { currentpoint AGMCORE_deltaY sub exch pop clippath pathbbox pop pop pop 44 add exch moveto } if AGMCORE_str256 0 AGMCORE_tmp getinterval show ( ) show } ifelse 0 1 AGMCORE_str256 length 1 sub { AGMCORE_str256 exch 0 put }for /AGMCORE_tmp 0 def } { dup 94 eq { pop AGMCORE_arg1 0 ge { AGMCORE_arg1 AGMCORE_str256 cvs dup /AGMCORE_tmp exch length def AGMCORE_str256 exch 0 exch putinterval AGMCORE_str256 0 AGMCORE_tmp getinterval stringwidth pop currentpoint pop add AGMCORE_deltaX { 28 add gt currentpoint AGMCORE_deltaY sub exch pop clippath pathbbox pop pop pop 44 add exch moveto } if AGMCORE_str256 0 AGMCORE_tmp getinterval show } { /AGMCORE_arg1 0 def } ifelse 0 1 AGMCORE_str256 length 1 sub { AGMCORE_str256 exch 0 put }for /AGMCORE_tmp 0 def AGMCORE_arg1 0 ne { /AGMCORE_arg1 AGMCORE_arg2 def } if } { AGMCORE_str256 exch AGMCORE_tmp exch put /AGMCORE_tmp AGMCORE_tmp 1 add def }ifelse } ifelse } forall } bdf level2{ /AGMCORE_map_reserved_ink_name { dup type /stringtype eq{ dup /Red eq{ pop (_Red_) }{ dup /Green eq{ pop (_Green_) }{ dup /Blue eq{ pop (_Blue_) }{ dup /Cyan eq{ pop (_Cyan_) }{ dup /Magenta eq{ pop (_Magenta_) }{ dup /Yellow eq{ pop (_Yellow_) }{ dup /Black eq{ pop (_Black_) }{ dup / eq{ pop (Process) }if }ifelse }ifelse }ifelse }ifelse }ifelse }ifelse }ifelse }def }if }if /doc_setup{ Adobe_AGM_Core begin /AGMCORE_will_host_separate xdf /AGMCORE_ps_version xdf /AGMCORE_ps_level xdf errordict /AGM_handleerror known not { errordict /AGM_handleerror errordict /handleerror get put errordict /handleerror { Adobe_AGM_Core begin $error /newerror get AGMCORE_cur_err null ne and {$error /newerror false put AGMCORE_cur_err /AGMCORE_bad_environ eq { /AGMCORE_bad_environ AGMCORE_ps_level AGMCORE_ps_version } { AGMCORE_cur_err 0 0 } ifelse compose_error_msg } if $error /newerror true put end errordict /AGM_handleerror get exec } bind put }if /AGMCORE_environ_ok ps_level AGMCORE_ps_level ge ps_version AGMCORE_ps_version ge and AGMCORE_ps_level -1 eq or def AGMCORE_environ_ok not {/AGMCORE_cur_err /AGMCORE_bad_environ def} if /AGMCORE_&setgray systemdict/setgray get def level2{ /AGMCORE_&setcolor systemdict/setcolor get def /AGMCORE_&setcolorspace systemdict/setcolorspace get def /AGMCORE_&&setcolorspace /setcolorspace ldf }if /AGMCORE_&image systemdict/image get def /AGMCORE_&imagemask systemdict/imagemask get def /colorimage where{ pop /AGMCORE_&colorimage /colorimage ldf }if /AGMCORE_in_rip_sep level2{ currentpagedevice/Separations 2 copy known{ }{ }{ get pop pop false }ifelse false }ifelse def level2 not{ /xput{ dup load dup length exch maxlength eq{ dup dup load dup length dup 0 eq {pop 1} if 2 mul dict copy def }if load begin def end }def }{ /xput{ load 3 1 roll put }def }ifelse /AGMCORE_gstate_known{ where{ /Adobe_AGM_Core_Id known }{ false }ifelse }ndf /AGMCORE_GSTATE AGMCORE_gstate_known not{ /AGMCORE_GSTATE 21 dict def /AGMCORE_tmpmatrix matrix def /AGMCORE_gstack 32 array def /AGMCORE_gstackptr 0 def /AGMCORE_gstacksaveptr 0 def /AGMCORE_gstackframekeys 7 def /AGMCORE_&gsave /gsave ldf /AGMCORE_&grestore /grestore ldf /AGMCORE_&grestoreall /grestoreall ldf /AGMCORE_&save /save ldf /AGMCORE_gdictcopy { begin { def } forall end }def /AGMCORE_gput { AGMCORE_gstack AGMCORE_gstackptr get 3 1 roll put }def /AGMCORE_gget { AGMCORE_gstack AGMCORE_gstackptr get exch get }def /gsave { AGMCORE_&gsave AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gstackptr 1 add dup 32 ge {limitcheck} if Adobe_AGM_Core exch /AGMCORE_gstackptr exch put AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gdictcopy }def /grestore { AGMCORE_&grestore AGMCORE_gstackptr 1 sub dup AGMCORE_gstacksaveptr lt {1 add} if Adobe_AGM_Core exch /AGMCORE_gstackptr exch put }def /grestoreall { AGMCORE_&grestoreall Adobe_AGM_Core /AGMCORE_gstackptr AGMCORE_gstacksaveptr put }def /save { AGMCORE_&save AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gstackptr 1 add dup 32 ge {limitcheck} if Adobe_AGM_Core begin /AGMCORE_gstackptr exch def /AGMCORE_gstacksaveptr AGMCORE_gstackptr def end AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gdictcopy }def 0 1 AGMCORE_gstack length 1 sub { AGMCORE_gstack exch AGMCORE_gstackframekeys dict put } for }if /currentcmykcolor [0 0 0 0] AGMCORE_gput /currentstrokeadjust false AGMCORE_gput /currentcolorspace [/DeviceGray] AGMCORE_gput /sep_tint 0 AGMCORE_gput /sep_colorspace_dict null AGMCORE_gput /indexed_colorspace_dict null AGMCORE_gput /currentcolor_intent () AGMCORE_gput end }def /page_setup { Adobe_AGM_Core begin /setcmykcolor { 4 copy AGMCORE_cmykbuf astore /currentcmykcolor exch AGMCORE_gput 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor pop }ndf /AGMCORE_ccimage_exists /customcolorimage where {pop true}{false} ifelse def /currentcmykcolor { /currentcmykcolor AGMCORE_gget aload pop }ndf /setoverprint { pop }ndf /currentoverprint { false }ndf /AGMCORE_deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt def /AGMCORE_cyan_plate 1 0 0 0 test_cmyk_color_plate def /AGMCORE_magenta_plate 0 1 0 0 test_cmyk_color_plate def /AGMCORE_yellow_plate 0 0 1 0 test_cmyk_color_plate def /AGMCORE_black_plate 0 0 0 1 test_cmyk_color_plate def /AGMCORE_plate_ndx AGMCORE_cyan_plate{ 0 }{ AGMCORE_magenta_plate{ 1 }{ AGMCORE_yellow_plate{ 2 }{ AGMCORE_black_plate{ 3 }{ 4 }ifelse }ifelse }ifelse }ifelse def /AGMCORE_composite_job AGMCORE_cyan_plate AGMCORE_magenta_plate and AGMCORE_yellow_plate and AGMCORE_black_plate and def /AGMCORE_producing_seps AGMCORE_composite_job not AGMCORE_in_rip_sep or def /AGMCORE_host_sep AGMCORE_producing_seps AGMCORE_in_rip_sep not and def /AGM_preserve_spots /AGM_preserve_spots where{ pop AGM_preserve_spots }{ systemdict/setdistillerparams known product (Adobe PostScript Parser) ne and AGMCORE_producing_seps or }ifelse def AGMCORE_host_sep AGMCORE_will_host_separate not and { /AGMCORE_cur_err /AGMCORE_color_space_onhost_seps def AGMCORE_color_space_onhost_seps }if /AGMCORE_avoid_L2_sep_space version cvr 2012 lt level2 and AGMCORE_producing_seps not and def /AGMCORE_is_cmyk_sep AGMCORE_cyan_plate AGMCORE_magenta_plate or AGMCORE_yellow_plate or AGMCORE_black_plate or def /AGM_avoid_0_cmyk where{ pop AGM_avoid_0_cmyk }{ AGM_preserve_spots }ifelse { /setcmykcolor[ {4 copy add add add 0 eq currentoverprint and{pop 0.0005}if}/exec cvx /setcmykcolor load dup type/operatortype ne{/exec cvx}if ]cvx def }if AGMCORE_host_sep{ /AGMCORE_get_ink_data AGMCORE_cyan_plate{ {pop pop pop} }{ AGMCORE_magenta_plate{ {4 3 roll pop pop pop} }{ AGMCORE_yellow_plate{ {4 2 roll pop pop pop} }{ {4 1 roll pop pop pop} }ifelse }ifelse }ifelse def }if AGMCORE_in_rip_sep{ /setcustomcolor { exch aload pop dup 7 1 roll inRip_spot_has_ink not { 4 {4 index mul 4 1 roll} repeat /DeviceCMYK setcolorspace 6 -2 roll pop pop }{ Adobe_AGM_Core begin /AGMCORE_k xdf /AGMCORE_y xdf /AGMCORE_m xdf /AGMCORE_c xdf end [/Separation 4 -1 roll /DeviceCMYK {dup AGMCORE_c mul exch dup AGMCORE_m mul exch dup AGMCORE_y mul exch AGMCORE_k mul} ] setcolorspace }ifelse setcolor }ndf /setseparationgray { [/Separation (All) /DeviceGray {}] setcolorspace_opt 1 exch sub setcolor }ndf }{ /setseparationgray { AGMCORE_&setgray }ndf }ifelse /findcmykcustomcolor { 5 makereadonlyarray }ndf /setcustomcolor { exch aload pop pop 4 {4 index mul 4 1 roll} repeat setcmykcolor pop }ndf /has_color /colorimage where{ AGMCORE_producing_seps{ pop true }{ systemdict eq }ifelse }{ false }ifelse def /map_index { 1 index mul exch getinterval {255 div} forall }def level2{ /mo /moveto ldf /ln /lineto ldf /cv /curveto ldf /knockout_unitsq { 1 setgray 0 0 1 1 rectfill }def /level2ScreenFreq{ begin 60 HalftoneType 1 eq{ pop Frequency }if HalftoneType 2 eq{ pop GrayFrequency }if HalftoneType 5 eq{ put repeat pop }def /currentScreenFreq{ currenthalftone level2ScreenFreq }def /invert_image_samples { Adobe_AGM_Core/AGMCORE_tmp Decode length ddf /Decode [ Decode 1 get Decode 0 get] def }def /knockout_image_samples { Operator/imagemask ne{ /Decode [1 1] def }if }def /get_gstate { AGMCORE_GSTATE begin /AGMCORE_GSTATE_ctm AGMCORE_tmpmatrix currentmatrix def /AGMCORE_GSTATE_clr_spc currentcolorspace def /AGMCORE_GSTATE_clr_indx 0 def /AGMCORE_GSTATE_clr_comps 12 array def mark currentcolor counttomark {AGMCORE_GSTATE_clr_comps AGMCORE_GSTATE_clr_indx 3 -1 roll /AGMCORE_GSTATE_clr_indx AGMCORE_GSTATE_clr_indx 1 add def} /AGMCORE_GSTATE_fnt rootfont def /AGMCORE_GSTATE_lw currentlinewidth def /AGMCORE_GSTATE_lc currentlinecap def /AGMCORE_GSTATE_lj currentlinejoin def /AGMCORE_GSTATE_ml currentmiterlimit def currentdash /AGMCORE_GSTATE_do xdf /AGMCORE_GSTATE_da xdf /AGMCORE_GSTATE_sa currentstrokeadjust def /AGMCORE_GSTATE_clr_rnd currentcolorrendering def /AGMCORE_GSTATE_op currentoverprint def /AGMCORE_GSTATE_bg currentblackgeneration cvlit def /AGMCORE_GSTATE_ucr currentundercolorremoval cvlit def currentcolortransfer cvlit /AGMCORE_GSTATE_gy_xfer xdf cvlit /AGMCORE_GSTATE_b_xfer xdf cvlit /AGMCORE_GSTATE_g_xfer xdf cvlit /AGMCORE_GSTATE_r_xfer xdf /AGMCORE_GSTATE_ht currenthalftone def /AGMCORE_GSTATE_flt currentflat def end }ndf }if end pop Default level2ScreenFreq /set_gstate { AGMCORE_GSTATE begin AGMCORE_GSTATE_ctm setmatrix AGMCORE_GSTATE_clr_spc setcolorspace AGMCORE_GSTATE_clr_indx {AGMCORE_GSTATE_clr_comps AGMCORE_GSTATE_clr_indx 1 sub get repeat setcolor /AGMCORE_GSTATE_clr_indx AGMCORE_GSTATE_clr_indx 1 sub def} AGMCORE_GSTATE_fnt setfont AGMCORE_GSTATE_lw setlinewidth AGMCORE_GSTATE_lc setlinecap AGMCORE_GSTATE_lj setlinejoin AGMCORE_GSTATE_ml setmiterlimit AGMCORE_GSTATE_da AGMCORE_GSTATE_do setdash AGMCORE_GSTATE_sa setstrokeadjust AGMCORE_GSTATE_clr_rnd setcolorrendering AGMCORE_GSTATE_op setoverprint AGMCORE_GSTATE_bg cvx setblackgeneration AGMCORE_GSTATE_ucr cvx setundercolorremoval AGMCORE_GSTATE_r_xfer cvx AGMCORE_GSTATE_g_xfer cvx AGMCORE_GSTATE_b_xfer cvx AGMCORE_GSTATE_gy_xfer cvx setcolortransfer AGMCORE_GSTATE_ht /HalftoneType get dup 9 eq exch 100 eq or { currenthalftone /HalftoneType get AGMCORE_GSTATE_ht /HalftoneType get ne { mark AGMCORE_GSTATE_ht {sethalftone} stopped cleartomark } if }{ AGMCORE_GSTATE_ht sethalftone } ifelse AGMCORE_GSTATE_flt setflat end }ndf AGMCORE_producing_seps not{ /setcolorspace where{ /Adobe_AGM_Core_Id known not }{ true }ifelse { /setcolorspace { dup type dup /arraytype eq exch /packedarraytype eq or{ dup 0 get dup /Separation eq{ pop [ exch {} forall ] dup dup 1 get AGMCORE_map_reserved_ink_name 1 exch put }{ /DeviceN eq { [ exch {} forall ] dup dup 1 get [ exch {AGMCORE_map_reserved_ink_name} forall ] 1 exch put }if }ifelse }if AGMCORE_&&setcolorspace }def }if }{ }if /adj { }def /mo{ }def /ln{ }def /cv{ currentstrokeadjust{ transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform }if adj moveto adj lineto 6 2 roll adj 6 2 roll adj 6 2 roll adj curveto }def /knockout_unitsq { 1 setgray 8 8 1 [8 0 0 8 0 0] {<ffffffffffffffff>} image }def /currentstrokeadjust{ /currentstrokeadjust AGMCORE_gget }def /setstrokeadjust{ /currentstrokeadjust exch AGMCORE_gput }def /currentScreenFreq{ currentscreen pop pop }def /invert_image_samples { {1 exch sub} currenttransfer addprocs settransfer }def /knockout_image_samples { { pop 1 } currenttransfer addprocs settransfer }def /setcolorspace { /currentcolorspace exch AGMCORE_gput } def /currentcolorspace { /currentcolorspace AGMCORE_gget } def /n_color_components { dup type /arraytype eq{ 0 get }if dup /DeviceGray eq{ pop 1 }{ /DeviceCMYK eq{ 4 }{ 3 }ifelse }ifelse } def /setcolor_devicecolor { dup type /arraytype eq{ 0 get }if dup /DeviceGray eq{ pop setgray }{ /DeviceCMYK eq{ setcmykcolor }{ setrgbcolor }ifelse }ifelse }def /setcolor { currentcolorspace 0 get dup /DeviceGray ne{ dup /DeviceCMYK ne{ dup /DeviceRGB ne{ dup /Separation eq{ pop currentcolorspace 3 get exec currentcolorspace 2 get }{ dup /Indexed eq{ pop currentcolorspace 3 get dup type /stringtype eq{ currentcolorspace 1 get n_color_components 3 -1 roll map_index }{ exec }ifelse currentcolorspace 1 get }{ /AGMCORE_cur_err /AGMCORE_invalid_color_space def AGMCORE_invalid_color_space }ifelse }ifelse }if }if }if } def }ifelse setcolor_devicecolor /op /setoverprint ldf /lw /setlinewidth ldf /lc /setlinecap ldf /lj /setlinejoin ldf /ml /setmiterlimit ldf /dsh /setdash ldf /sadj /setstrokeadjust ldf /gry /setgray ldf /rgb /setrgbcolor ldf /cmyk /setcmykcolor ldf /sep /setsepcolor ldf /idx /setindexedcolor ldf /colr /setcolor ldf /csacrd /set_csa_crd ldf /sepcs /setsepcolorspace ldf /idxcs /setindexedcolorspace ldf /cp /closepath ldf /clp /clp_npth ldf /eclp /eoclp_npth ldf /spclp /stkpath_clp_npth ldf /f /fill ldf /ef /eofill ldf /s /stroke ldf /sclp /stk_n_clp_npth ldf /nclp /npth_clp ldf /img /imageormask ldf /sepimg /sep_imageormask ldf /idximg /indexed_imageormask ldf /gset /graphic_setup ldf /gcln /graphic_cleanup ldf currentdict{ dup xcheck 1 index type dup /arraytype eq exch /packedarraytype eq or }if def }forall bind and { }def /page_trailer { end }def /unload{ systemdict/languagelevel known{ systemdict/languagelevel get 2 ge{ userdict/Adobe_AGM_Core 2 copy known{ undef }{ pop pop }ifelse }if }if }def /doc_trailer{ }def systemdict /findcolorrendering known{ /findcolorrendering systemdict /findcolorrendering get def }if systemdict /setcolorrendering known{ /setcolorrendering systemdict /setcolorrendering get def }if /test_cmyk_color_plate { gsave setcmykcolor currentgray 1 ne grestore }def /inRip_spot_has_ink { Adobe_AGM_Core/AGMCORE_name xddf false currentpagedevice/SeparationColorNames get{ AGMCORE_name eq or }forall }def /current_ink { dup length 0 eq{ pop true }{ Adobe_AGM_Core/ink_result false put { dup /ProcessCyan eq{ AGMCORE_cyan_plate ink_result or Adobe_AGM_Core/ink_result xddf }{ dup /ProcessMagenta eq{ AGMCORE_magenta_plate ink_result or Adobe_AGM_Core/ink_result xddf }{ dup /ProcessYellow eq{ AGMCORE_yellow_plate ink_result or Adobe_AGM_Core/ink_result xddf }{ dup /ProcessBlack eq{ AGMCORE_black_plate ink_result or Adobe_AGM_Core/ink_result xddf }{ dup /sep_colorspace_dict AGMCORE_gget dup null eq{ pop false ink_result or Adobe_AGM_Core/ink_result xddf }{ /Name get eq{ 1 setsepcolor currentgray 1 ne ink_result or Adobe_AGM_Core/ink_result xddf }{ false ink_result or Adobe_AGM_Core/ink_result xddf }ifelse }ifelse }ifelse }def /map255_to_range { 1 index sub 3 -1 roll 255 div mul add }def /set_csa_crd { /sep_colorspace_dict null AGMCORE_gput begin CSA map_csa setcolorspace_opt set_crd end } def /setsepcolor { /sep_colorspace_dict AGMCORE_gget begin dup /sep_tint exch AGMCORE_gput TintProc end }ifelse }ifelse }ifelse pop } forall ink_result }ifelse } def /sep_colorspace_proc { Adobe_AGM_Core/AGMCORE_tmp xddf /sep_colorspace_dict AGMCORE_gget begin currentdict/Components known{ Components aload pop TintMethod/Lab eq{ 2 {AGMCORE_tmp mul NComponents 1 roll} repeat LMax sub AGMCORE_tmp mul LMax add NComponents 1 roll }{ TintMethod/Subtractive eq{ NComponents{ AGMCORE_tmp mul NComponents 1 roll }repeat }{ NComponents{ 1 sub AGMCORE_tmp mul 1 add NComponents 1 roll } repeat }ifelse }ifelse }{ ColorLookup AGMCORE_tmp ColorLookup length 1 sub mul round cvi get aload pop }ifelse end } def /sep_colorspace_gray_proc { Adobe_AGM_Core/AGMCORE_tmp xddf } def /sep_proc_name { dup 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or level2 not and has_color not and{ pop [/DeviceGray] /sep_colorspace_gray_proc }{ /sep_colorspace_proc }ifelse } def /setsepcolorspace { dup /sep_colorspace_dict exch AGMCORE_gput begin /MappedCSA CSA map_csa def Adobe_AGM_Core/AGMCORE_sep_special Name dup () eq exch (All) eq or ddf AGMCORE_avoid_L2_sep_space{ [/Indexed MappedCSA sep_proc_name 255 exch { 255 div } /exec cvx 3 -1 roll [ 4 1 roll load /exec cvx ] cvx ] setcolorspace_opt /TintProc { 255 mul setcolor }bdf }{ MappedCSA 0 get /DeviceCMYK eq currentdict/Components known and AGMCORE_sep_special not and{ /TintProc [ Components aload pop Name findcmykcustomcolor /exch cvx /setcustomcolor cvx ] cvx bdf }{ AGMCORE_host_sep Name (All) eq and{ /TintProc { 1 exch sub setseparationgray }bdf }{ AGMCORE_in_rip_sep MappedCSA 0 get /DeviceCMYK eq and AGMCORE_host_sep or Name () eq and{ /TintProc [ MappedCSA sep_proc_name exch 0 get /DeviceCMYK }{ cvx /setcmykcolor cvx /sep_colorspace_dict AGMCORE_gget begin GrayLookup AGMCORE_tmp GrayLookup length 1 sub mul round cvi get end eq{ }{ cvx /setgray cvx }ifelse ] cvx bdf AGMCORE_producing_seps MappedCSA 0 get dup /DeviceCMYK eq exch /DeviceGray eq or and AGMCORE_sep_special not and{ /TintProc [ /dup cvx MappedCSA sep_proc_name cvx exch 0 get /DeviceGray eq{ 1 /exch cvx /sub cvx 0 0 0 4 -1 /roll cvx cvx }if /Name cvx /findcmykcustomcolor cvx /exch AGMCORE_host_sep{ AGMCORE_is_cmyk_sep }{ Name inRip_spot_has_ink not }ifelse { /pop cvx 1 }if /setcustomcolor cvx ] cvx bdf /TintProc /setcolor ldf load ] setcolorspace_opt [/Separation Name MappedCSA sep_proc_name }{ }ifelse }ifelse }ifelse }ifelse }ifelse set_crd 1 setsepcolor end } def /setindexedcolorspace { dup /indexed_colorspace_dict exch AGMCORE_gput begin /MappedCSA CSA map_csa def AGMCORE_host_sep level2 not and{ 0 0 0 0 setcmykcolor }{ [/Indexed MappedCSA level2 not has_color not and{ dup 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or{ pop [/DeviceGray] }if HiVal GrayLookup }{ HiVal currentdict/RangeArray known{ { /indexed_colorspace_dict AGMCORE_gget begin Lookup exch dup HiVal gt{ pop HiVal }if NComponents mul NComponents getinterval {} forall NComponents 1 sub -1 0{ RangeArray exch 2 mul 2 getinterval aload pop map255_to_range }for end } bind Lookup }ifelse }ifelse ] setcolorspace_opt set_crd }ifelse }{ NComponents 1 roll end }def /setindexedcolor { AGMCORE_host_sep{ /indexed_colorspace_dict AGMCORE_gget/Lookup get 4 3 -1 roll map_index setcmykcolor }{ setcolor }ifelse } def /imageormask_sys { begin save mark level2{ currentdict Operator /imagemask eq{ AGMCORE_&imagemask }{ AGMCORE_&image }ifelse }{ Width Height Operator /imagemask eq{ Decode 0 get 1 eq Decode 1 get 0 eq and ImageMatrix /DataSource load AGMCORE_&imagemask }{ BitsPerComponent ImageMatrix /DataSource load AGMCORE_&image }ifelse }ifelse cleartomark restore end }def /overprint_plate { currentoverprint{ 0 get dup /DeviceGray eq{ pop AGMCORE_black_plate not }{ /DeviceCMYK eq{ AGMCORE_is_cmyk_sep not }if }ifelse }{ }def /rdline { currentfile AGMCORE_str256 readline pop } def /rdcmntline { currentfile AGMCORE_str256 readline pop (%) anchorsearch {pop} if } def /filter_cmyk { dup type /filetype ne{ 0 () /SubFileDecode filter }if [ exch { AGMCORE_src256 readstring pop dup length /AGMCORE_srcLen exch def /AGMCORE_ndx 0 def AGMCORE_plate_ndx 4 AGMCORE_srcLen 1 sub{ 1 index exch get AGMCORE_dst64 AGMCORE_ndx 3 -1 roll put /AGMCORE_ndx AGMCORE_ndx 1 add def }for pop AGMCORE_dst64 0 AGMCORE_ndx getinterval } bind /exec cvx ] cvx } def /imageormask { begin SkipImageProc not{ save mark level2 AGMCORE_host_sep not and{ currentdict Operator /imagemask eq{ imagemask }{ AGMCORE_in_rip_sep currentoverprint and currentcolorspace 0 get /DeviceGray eq and{ [/Separation /Black /DeviceGray {}] setcolorspace /Decode [ Decode 1 get Decode 0 get ] def }if image }ifelse }{ Width Height Operator /imagemask eq{ Decode 0 get 1 eq Decode 1 get 0 eq and ImageMatrix /DataSource load AGMCORE_host_sep{ false }ifelse imageormask_sys }{ }{ currentgray 1 ne{ currentdict imageormask_sys }{ currentoverprint not{ 1 AGMCORE_&setgray knockout_image_samples currentdict imageormask_sys }{ nulldevice currentdict }ifelse }ifelse imagemask }ifelse BitsPerComponent ImageMatrix MultipleDataSources{ 0 1 NComponents 1 sub{ DataSource exch get }for }{ /DataSource load }ifelse Operator /colorimage eq{ AGMCORE_host_sep{ MultipleDataSources level2 or NComponents MultipleDataSources{ 4 {pop} repeat /DataSource [ DataSource 0 get /exec 4 eq and{ cvx cvx cvx cvx cvx }{ filter_cmyk 0 () /SubFileDecode filter def DataSource 1 get /exec DataSource 2 get /exec DataSource 3 get /exec /AGMCORE_get_ink_data ] cvx def /DataSource /DataSource load }ifelse /Decode [ Decode 0 get Decode 1 get ] def /MultipleDataSources false def /NComponents 1 def /Operator /image def AGMCORE_is_cmyk_sep{ currentoverprint InksUsed nulldevice }{ invert_image_samples }ifelse current_ink not and{ }{ }{ currentoverprint not{ knockout_image_samples }{ nulldevice }ifelse }ifelse 1 AGMCORE_&setgray currentdict imageormask_sys currentcolortransfer {pop 1} exch addprocs 4 1 roll {pop 1} exch addprocs 4 1 roll {pop 1} exch addprocs 4 1 roll {pop 1} exch addprocs 4 1 roll setcolortransfer MultipleDataSources NComponents AGMCORE_&colorimage }{ }{ }ifelse true NComponents colorimage }ifelse Operator /image eq{ AGMCORE_host_sep{ HostSepColorImage{ invert_image_samples }{ AGMCORE_black_plate not{ currentoverprint not{ knockout_image_samples }{ nulldevice }ifelse }if }ifelse 1 AGMCORE_&setgray currentdict imageormask_sys }{ }{ image }ifelse Operator/knockout eq{ pop pop pop pop pop currentoverprint InksUsed }{ currentcolorspace knockout_unitsq }if }ifelse }if }ifelse }ifelse current_ink not and{ overprint_plate not{ }if end }ifelse }ifelse cleartomark restore }def /tint_image_to_color { begin Width Height BitsPerComponent ImageMatrix /DataSource load end Adobe_AGM_Core begin /AGMCORE_mbuf 0 string def /AGMCORE_ybuf 0 string def /AGMCORE_kbuf 0 string def { colorbuf dup length AGMCORE_mbuf length ne { dup length dup dup /AGMCORE_mbuf exch string def /AGMCORE_ybuf exch string def /AGMCORE_kbuf exch string def } if dup AGMCORE_mbuf copy AGMCORE_ybuf copy AGMCORE_kbuf copy pop } addprocs {AGMCORE_mbuf}{AGMCORE_ybuf}{AGMCORE_kbuf} true 4 colorimage end } def /sep_imageormask_lev1 { begin MappedCSA 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or has_color not and{ { 255 mul round cvi GrayLookup exch get } currenttransfer addprocs settransfer currentdict imageormask }{ /sep_colorspace_dict AGMCORE_gget/Components known{ MappedCSA 0 get /DeviceCMYK eq{ Components aload pop }{ 0 0 0 Components aload pop 1 exch sub }ifelse Adobe_AGM_Core/AGMCORE_k Adobe_AGM_Core/AGMCORE_y Adobe_AGM_Core/AGMCORE_m Adobe_AGM_Core/AGMCORE_c xddf xddf xddf xddf settransfer AGMCORE_y 0.0 eq AGMCORE_m 0.0 eq and AGMCORE_c 0.0 eq and{ {AGMCORE_k mul 1 exch sub} currenttransfer addprocs }{ currentdict imageormask currentcolortransfer {AGMCORE_k mul 1 exch sub} exch {AGMCORE_y mul 1 exch sub} exch {AGMCORE_m mul 1 exch sub} exch {AGMCORE_c mul 1 exch sub} exch setcolortransfer currentdict tint_image_to_color }ifelse }{ addprocs addprocs addprocs addprocs 4 4 4 4 1 1 1 1 roll roll roll roll MappedCSA 0 get /DeviceGray eq { {255 mul round cvi ColorLookup exch get 0 currenttransfer addprocs settransfer currentdict imageormask }{ MappedCSA 0 get /DeviceCMYK eq { currentcolortransfer {255 mul round cvi ColorLookup exch exch sub} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch exch sub} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch exch sub} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch exch sub} exch addprocs 4 1 roll setcolortransfer currentdict tint_image_to_color }{ currentcolortransfer {pop 1} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch exch addprocs 4 1 roll setcolortransfer currentdict tint_image_to_color }ifelse }ifelse }ifelse }ifelse end }def /sep_image_lev1_sep { begin /sep_colorspace_dict AGMCORE_gget/Components known{ Components aload pop Adobe_AGM_Core/AGMCORE_k Adobe_AGM_Core/AGMCORE_y Adobe_AGM_Core/AGMCORE_m Adobe_AGM_Core/AGMCORE_c {AGMCORE_c {AGMCORE_m {AGMCORE_y {AGMCORE_k mul mul mul mul 1 1 1 1 exch exch exch exch xddf xddf xddf xddf get} get 3 get 1 get 2 get 1 get 1 get 1 get 0 get 1 get 2 get} get 1 get} get 0 get} sub} sub} sub} sub} }{ {255 {255 {255 {255 }ifelse mul mul mul mul round round round round cvi cvi cvi cvi ColorLookup ColorLookup ColorLookup ColorLookup exch exch exch exch get get get get 0 1 2 3 get get get get 1 1 1 1 exch exch exch exch sub} sub} sub} sub} AGMCORE_get_ink_data currenttransfer addprocs settransfer currentdict imageormask_sys end }def /sep_imageormask { /sep_colorspace_dict AGMCORE_gget begin /MappedCSA CSA map_csa def begin SkipImageProc not{ save mark AGMCORE_avoid_L2_sep_space{ /Decode [ Decode 0 get 255 mul Decode 1 get 255 mul ] def }if AGMCORE_ccimage_exists MappedCSA 0 get /DeviceCMYK eq and currentdict/Components known and Name () ne and Name (All) ne and Operator /image eq and AGMCORE_producing_seps not and level2 not and { Width Height BitsPerComponent ImageMatrix [ /DataSource load /exec cvx { 0 1 2 index length 1 sub{ 1 index exch 2 copy get 255 xor put }for } /exec cvx ] cvx bind MappedCSA 0 get /DeviceCMYK eq{ Components aload pop }{ 0 0 0 Components aload pop 1 exch sub }ifelse Name findcmykcustomcolor customcolorimage }{ AGMCORE_producing_seps not{ level2{ AGMCORE_avoid_L2_sep_space not currentcolorspace 0 get /Separation ne and{ [/Separation Name MappedCSA sep_proc_name load ] setcolorspace_opt /sep_tint AGMCORE_gget setcolor }if }{ currentdict imageormask }{ currentdict Operator /imagemask eq{ imageormask }{ sep_imageormask_lev1 }ifelse }ifelse AGMCORE_host_sep{ Operator/knockout eq{ currentoverprint InksUsed current_ink not and{ }{ currentdict/ImageMatrix get concat knockout_unitsq }ifelse }{ currentgray 1 ne{ AGMCORE_is_cmyk_sep Name (All) ne and{ level2{ [ /Separation Name [/DeviceGray] AGMCORE_get_ink_data { sep_colorspace_proc 1 exch sub } bind ] AGMCORE_&setcolorspace /sep_tint AGMCORE_gget AGMCORE_&setcolor }{ currentdict imageormask_sys currentdict Operator /imagemask eq{ imageormask_sys }{ sep_image_lev1_sep }ifelse }ifelse }{ Operator/imagemask ne{ invert_image_samples }if currentdict imageormask_sys }ifelse currentoverprint not Name (All) eq or{ knockout_image_samples }{ nulldevice }ifelse currentdict imageormask_sys }ifelse }ifelse currentcolorspace 0 get /Separation ne{ [/Separation Name MappedCSA sep_proc_name }{ }{ load ] setcolorspace_opt /sep_tint AGMCORE_gget setcolor }if currentoverprint MappedCSA 0 get /DeviceCMYK eq and Name inRip_spot_has_ink not and Name (All) ne and { imageormask_l2_overprint }{ currentdict imageormask }ifelse }ifelse }ifelse }ifelse cleartomark restore }if end end }def /modify_halftone_xfer { currenthalftone dup length dict copy begin currentdict 2 index known{ 1 index load dup length dict copy begin currentdict/TransferFunction known{ /TransferFunction load }{ currenttransfer }ifelse addprocs /TransferFunction xdf currentdict end def currentdict end sethalftone }{ currentdict/TransferFunction known{ /TransferFunction load }{ currenttransfer }ifelse addprocs /TransferFunction xdf currentdict end sethalftone pop }ifelse }def /read_image_file { AGMCORE_imagefile 0 setfileposition dup /DataSource {AGMCORE_imagefile AGMCORE_imbuf readstring pop} put exch load exec }def /write_image_file { { (AGMCORE_imagefile) (w+) file } stopped{ false }{ Adobe_AGM_Core/AGMCORE_imagefile xddf Adobe_AGM_Core/AGMCORE_imbuf Width BitsPerComponent mul 7 add 8 idiv string ddf 1 1 Height { pop DataSource dup type /filetype eq{ AGMCORE_imbuf readstring pop }{ exec } ifelse AGMCORE_imagefile exch writestring }for true }ifelse }def /imageormask_l2_overprint { write_image_file{ currentcmykcolor 0 ne{ [/Separation /Black /DeviceGray {}] setcolorspace gsave /Black [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 1 roll pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore }if 0 ne{ [/Separation /Yellow /DeviceGray {}] setcolorspace gsave /Yellow [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 2 roll pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore }if 0 ne{ [/Separation /Magenta /DeviceGray {}] setcolorspace gsave /Magenta [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 3 roll pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore }if 0 ne{ [/Separation /Cyan /DeviceGray {}] setcolorspace gsave /Cyan [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore } if AGMCORE_imagefile closefile (AGMCORE_imagefile) deletefile }{ currentdict imageormask }ifelse } def /indexed_imageormask { begin save mark currentdict AGMCORE_host_sep{ Operator/knockout eq{ /indexed_colorspace_dict AGMCORE_gget /CSA get map_csa overprint_plate not{ knockout_unitsq }if }{ AGMCORE_is_cmyk_sep{ Operator /imagemask eq{ imageormask_sys }{ level2{ indexed_image_lev2_sep }{ indexed_image_lev1_sep }ifelse }ifelse }{ currentoverprint not{ knockout_image_samples imageormask_sys }{ nulldevice currentdict imageormask_sys }ifelse }ifelse }ifelse }{ level2{ imageormask }{ Operator /imagemask eq{ imageormask }{ indexed_imageormask_lev1 }ifelse }ifelse }ifelse cleartomark restore end }def /indexed_imageormask_lev1 { /indexed_colorspace_dict AGMCORE_gget begin begin currentdict MappedCSA 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or has_color not and{ {HiVal mul round cvi GrayLookup exch get HiVal div} currenttransfer addprocs settransfer imageormask }{ MappedCSA 0 get /DeviceGray eq { {HiVal mul round cvi Lookup exch get HiVal div} currenttransfer addprocs settransfer imageormask }{ MappedCSA 0 get /DeviceCMYK eq { currentcolortransfer {4 mul HiVal mul round cvi 3 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll {4 mul HiVal mul round cvi 2 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll {4 mul HiVal mul round cvi 1 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll {4 mul HiVal mul round cvi Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll setcolortransfer tint_image_to_color }{ currentcolortransfer {pop 1} exch addprocs 4 1 roll {3 mul HiVal mul round cvi 2 add Lookup exch get HiVal div} exch addprocs 4 1 roll {3 mul HiVal mul round cvi 1 add Lookup exch get HiVal div} exch addprocs 4 1 roll {3 mul HiVal mul round cvi Lookup exch get HiVal div} exch addprocs 4 1 roll setcolortransfer tint_image_to_color }ifelse }ifelse }ifelse end end }def /indexed_image_lev1_sep { /indexed_colorspace_dict AGMCORE_gget begin begin {4 mul HiVal mul round cvi Lookup exch get HiVal div 1 exch sub} {4 mul HiVal mul round cvi 1 add Lookup exch get HiVal div 1 exch sub} {4 mul HiVal mul round cvi 2 add Lookup exch get HiVal div 1 exch sub} {4 mul HiVal mul round cvi 3 add Lookup exch get HiVal div 1 exch sub} AGMCORE_get_ink_data currenttransfer addprocs settransfer currentdict imageormask_sys end end }def /indexed_image_lev2_sep { /indexed_colorspace_dict AGMCORE_gget begin begin currentcolorspace dup 1 /DeviceGray put dup 3 [ currentcolorspace 3 get { exch 4 mul 4 getinterval {} forall AGMCORE_get_ink_data 255 div 1 exch sub } /exec cvx ] cvx put setcolorspace currentdict Operator /imagemask eq{ AGMCORE_&imagemask }{ AGMCORE_&image }ifelse end end }def /add_csa { Adobe_AGM_Core begin /AGMCORE_CSA_cache xput end }def /map_csa { dup type /nametype eq{ Adobe_AGM_Core/AGMCORE_CSA_cache get exch get }if }def /add_csd { Adobe_AGM_Core begin /AGMCORE_CSD_cache xput end }def /get_csd { dup type /nametype eq{ Adobe_AGM_Core/AGMCORE_CSD_cache get exch get }if }def /add_pattern { Adobe_AGM_Core begin /AGMCORE_pattern_cache xput end }def /get_pattern { dup type /nametype eq{ Adobe_AGM_Core/AGMCORE_pattern_cache get exch get }if }def /set_pattern { dup /PatternType get 1 eq{ dup /PaintType get 1 eq{ false op [/DeviceGray] setcolorspace 0 setgray }if }if setpattern }def /setcolorspace_opt { dup currentcolorspace eq{ pop }{ setcolorspace }ifelse }def /updatecolorrendering { currentcolorrendering/Intent known{ currentcolorrendering/Intent get }{ null }ifelse Intent ne{ false Intent AGMCORE_CRD_cache { exch pop begin dup Intent eq{ currentdict setcolorrendering_opt end exch pop true exch exit }if end } forall pop not{ systemdict /findcolorrendering known{ Intent findcolorrendering pop /ColorRendering findresource dup length dict copy setcolorrendering_opt }if }if }if } def /add_crd { AGMCORE_CRD_cache 3 1 roll put }def /set_crd { AGMCORE_host_sep not level2 and{ currentdict/CRD known{ AGMCORE_CRD_cache CRD get dup null ne{ setcolorrendering_opt }{ pop }ifelse }{ currentdict/Intent known{ updatecolorrendering }if }ifelse }if }def /setcolorrendering_opt { dup currentcolorrendering eq{ pop }{ begin /Intent Intent def currentdict end setcolorrendering }ifelse }def /OPIimage { dup type /dicttype ne{ 10 dict begin /DataSource xdf /ImageMatrix xdf /BitsPerComponent xdf /Height xdf /Width xdf /MultipleDataSources false def /NComponents 1 def /ImageType 1 def /Decode [0 1 def] /SkipImageProc {false} def currentdict end }if dup begin /HostSepColorImage false def currentdict/Decode known not{ /Decode [ 0 currentcolorspace 0 get /Indexed eq{ 2 BitsPerComponent exp 1 sub }{ 1 }ifelse ] def }if currentdict/Operator known not{ /Operator /image def }if end /sep_colorspace_dict AGMCORE_gget null eq{ imageormask }{ gsave dup begin invert_image_samples end sep_imageormask grestore }ifelse }def /cpaint_gcomp { AGM_preserve_spots{ gsave nulldevice }if }def /cpaint_gsep { AGM_preserve_spots{ grestore currentoverprint Adobe_AGM_Core/AGMCORE_ovp xddf }{ gsave nulldevice }ifelse }def /cpaint_gend { AGM_preserve_spots{ Adobe_AGM_Core/AGMCORE_ovp get setoverprint }{ grestore }ifelse newpath }def /AGMCORE_ctm_stack bdict /push_ctm { stack length size le{ stack dup length 2 mul array dup /stack exch def copy pop }if stack size 3 -1 roll put /size size 1 add def } /pop_ctm { /size size 1 sub def size 0 lt{ /size 0 def }if stack size get } /stack 1 array /size 0 edict def /save_ctm { matrix currentmatrix AGMCORE_ctm_stack begin push_ctm end }def /restore_ctm { AGMCORE_ctm_stack begin pop_ctm end setmatrix }def /path_rez { dup 0 ne{ AGMCORE_deviceDPI exch div dup 1 lt{ pop 1 }if setflat }{ pop }ifelse }def end systemdict /setpacking known { setpacking } if %%EndResource %%BeginResource: procset Adobe_CoolType_Core 1.1 0 %%Copyright: Copyright 1997-1999 Adobe Systems Incorporated. All Rights Reserved. %%Version: 1.1 0 userdict/Adobe_CoolType_Core 40 dict dup begin put/Level2? systemdict /languagelevel known dup{pop systemdict/languagelevel get 2 ge}if def Level2? not{/currentglobal false def/setglobal/pop load def/gcheck{pop false}bind def /currentpacking false def/setpacking/pop load def}if currentpacking true setpacking/bdf{bind def}bind def/ldf{load def}bind def/doc_setup{ Adobe_CoolType_Core begin/mov/moveto ldf/nfnt/newencodedfont ldf/mfnt/makefont ldf/sfnt/setfont ldf/ufnt/undefinefont ldf/chp/charpath ldf/awsh/awidthshow ldf/wsh/widthshow ldf/ash/ashow ldf/sh/show ldf end userdict /Adobe_CoolType_Data 2 dict dup begin/WidthShowArray 256 array def /GenFauxMMInst{}bind def end put}bind def/doc_trailer{currentdict Adobe_CoolType_Core eq{end}if Adobe_CoolType_Core/unload get exec systemdict /undef known{userdict/Adobe_CoolType_Data undef}if}bind def/page_setup{ Adobe_CoolType_Core begin}bind def/page_trailer{end}bind def/unload{systemdict /languagelevel known{systemdict/languagelevel get 2 ge{userdict /Adobe_CoolType_Core 2 copy known{undef}{pop pop}ifelse}if}if}bind def/ndf{1 index where{pop pop pop}{dup xcheck{bind}if def}ifelse}def/findfont dup systemdict begin userdict begin/globaldict where{/globaldict get begin}if dup where pop exch get/globaldict where{pop end}if end end def/systemfindfont /findfont load def/undefinefont{pop}ndf/copyfont{currentglobal 3 1 roll 1 index gcheck setglobal dup null eq{0}{dup length}ifelse 2 index length add 1 add dict begin exch{1 index/FID eq{pop pop}{def}ifelse}forall dup null eq{pop} {{def}forall}ifelse currentdict end exch setglobal}bdf/newencodedfont{findfont dup length dict begin{1 index/FID ne{def}{pop pop}ifelse}forall/Encoding exch def currentdict end definefont pop}bdf/scff{$SubstituteFont begin dup type /stringtype eq{dup length exch}{null}ifelse/$sname exch def/$slen exch def /$fontname 1 index dup type/stringtype eq{cvn}if def/$used false def end findfont $SubstituteFont begin$used{currentglobal exch dup gcheck setglobal null copyfont begin/FontName $fontname def/currentdistillerparams where{pop}{ /FontInfo currentdict/FontInfo known{FontInfo null copyfont}{2 dict}ifelse dup begin/ItalicAngle$italicangle def/FontMatrix FontMatrix[1 0 ItalicAngle dup sin exch cos div 1 0 0]matrix concatmatrix readonly end 4 2 roll def def} ifelse FontName currentdict end definefont exch setglobal}if/$sname null def /$slen 0 def end}bdf/ConcatStrings{dup 0 exch{length add}forall string exch 0 exch{3 copy putinterval length add}forall pop}bind def/BeginFauxMMFont{1 index findfont pop 2 array astore ConcatStrings 3 1 roll($)exch 3 array astore ConcatStrings exch findfont currentglobal exch dup gcheck setglobal null copyfont/tempfontname exch definefont pop exch 12 dict begin/FontName exch def /FontType 0 def/FMapType 6 def/FontMatrix matrix def/PaintType 0 def}bind def /EndFauxMMFont{currentdict end dup/FontName get exch definefont exch setglobal exch mfnt sfnt}bind def/GenFauxMMInst{Adobe_CoolType_Data/GenFauxMMInst get exec}bind def/DefFauxMMInst{Adobe_CoolType_Data exch/GenFauxMMInst exch bind put}bind def/WSALoop{4 copy 1 index add 1 sub 1 exch{3 copy put pop 1 add}for pop pop 3 2 roll add exch 256 add}bind def/BuildWidthShowArray{currentfont begin FontType 0 eq dup{pop FMapType 6 eq}if{SubsVector dup length 1 sub 1 exch getinterval}{()}ifelse end Adobe_CoolType_Data/WidthShowArray get 0 0 4 3 roll{WSALoop}forall 256 2 index sub WSALoop pop pop pop}bind def/wsa{ Adobe_CoolType_Data/WidthShowArray get}bind def/?set{$SubstituteFont begin /$used false def/$fontname 4 index def end 3 index findfont $SubstituteFont begin$used{false}{dup/FontName known{dup/FontName get $fontname eq 1 index /DistillerFauxFont known not and}{false}ifelse}ifelse exch pop end{exch pop exch pop exch 2 dict dup/Found 3 index put exch findfont exch}{exch exec exch findfont 2 dict dup/Downloaded 6 5 roll put}ifelse dup/FontName 4 index put copyfont definefont pop}bind def/?str1 256 string def/?str2 256 string def /?add{1 index type/integertype eq{exch true 4 2}{false 3 1}ifelse roll 1 index findfont/Downloaded known{exec exch{exch ?str2 cvs exch findfont/Downloaded get 1 dict begin/Downloaded 1 index def ?str1 cvs length ?str1 1 index 1 add 3 index putinterval exch length 1 add 1 index add ?str1 2 index(*)putinterval ?str1 0 2 index getinterval cvn findfont ?str1 3 index(+)putinterval 2 dict dup/FontName ?str1 0 6 index getinterval cvn put dup/Downloaded Downloaded put end copyfont dup/FontName get exch definefont pop pop pop}{pop}ifelse}{pop exch{findfont dup/Found get dup length exch ?str1 cvs pop ?str1 1 index(+) putinterval ?str1 1 index 1 add 4 index ?str2 cvs putinterval ?str1 exch 0 exch 5 4 roll ?str2 cvs length 1 add add getinterval cvn 1 dict exch 1 index exch/FontName exch put copyfont dup/FontName get exch definefont pop}{pop} ifelse}ifelse}bind def/?sh{currentfont/Downloaded known{exch}if pop}bind def /?chp{currentfont/Downloaded known{pop}{false chp}ifelse}bind def/?mv{ currentfont/Downloaded known{moveto pop pop}{pop pop moveto}ifelse}bind def setpacking end userdict/$SubstituteFont 20 dict put 1 dict begin /SubstituteFont dup $error exch 2 copy known{get}{pop pop{pop/Courier}bind} ifelse def/currentdistillerparams where dup{pop pop currentdistillerparams /CannotEmbedFontPolicy 2 copy known{get/Error eq}{pop pop false}ifelse}if not{ countdictstack array dictstack 0 get begin userdict begin$SubstituteFont begin/$str 128 string def/$fontpat 128 string def/$slen 0 def/$sname null def /$match false def/$fontname null def/$used false def/$fontname null def /$italicangle 26.5 def/$findfontByEnum{dup/$fontname exch def$sname null eq{ $str cvs dup length$slen sub $slen getinterval}{pop$sname}ifelse $fontpat dup 0(fonts/*)putinterval exch 7 exch putinterval/$match false def mark{ $fontpat 0$slen 7 add getinterval{/$match exch def exit}$str filenameforall} stopped cleartomark/$slen 0 def$match false ne{$match(fonts/)anchorsearch pop pop cvn}{/Courier}ifelse}bind def/$ROS 1 dict dup begin/Adobe 4 dict dup begin /Japan1[/Ryumin-Light/HeiseiMin-W3/GothicBBB-Medium/HeiseiKakuGo-W5 /HeiseiMaruGo-W4/Jun101-Light]def/Korea1[/HYSMyeongJo-Medium/HYGoThic-Medium] def/GB1[/STSong-Light/STHeiti-Regular]def/CNS1[/MKai-Medium/MHei-Medium]def end def end def/$cmapname null def/$buildfontname{length $str 1 index(-) putinterval 1 add$str 1 index $cmapname$fontpat cvs putinterval $cmapname length add$str exch 0 exch getinterval cvn}bind def/$findfontByROS{/$fontname exch def $ROS Registry 2 copy known{get Ordering 2 copy known{get}{pop pop[]} ifelse}{pop pop[]}ifelse false exch{dup/CIDFont resourcestatus{pop pop save 1 index/CIDFont findresource dup/WidthsOnly known{dup/WidthsOnly get}{false} ifelse exch pop exch restore{pop}{exch pop true exit}ifelse}{pop}ifelse}forall {$str cvs $buildfontname}{false(*){save exch dup/CIDFont findresource dup /WidthsOnly known{dup/WidthsOnly get not}{true}ifelse exch/CIDSystemInfo get dup/Registry get Registry eq exch/Ordering get Ordering eq and and{exch restore exch pop true exit}{pop restore}ifelse}$str/CIDFont resourceforall{ $buildfontname}{$fontname $findfontByEnum}ifelse}ifelse}bind def end end currentdict/$error known currentdict/languagelevel known and dup{pop $error /SubstituteFont known}if dup{$error}{Adobe_CoolType_Core}ifelse begin{ /SubstituteFont/CMap/Category resourcestatus{pop pop{$SubstituteFont begin /$used true def dup length $slen gt$sname null ne or $slen 0 gt and{$sname null eq{dup $str cvs dup length$slen sub $slen getinterval cvn}{$sname}ifelse dup/CMap resourcestatus{pop pop dup/$cmapname exch def/CMap findresource /CIDSystemInfo get{def}forall$findfontByROS}{pop $findfontByEnum}ifelse}{ //SubstituteFont exec}ifelse/$slen 0 def end}}{{$SubstituteFont begin/$used true def dup length $slen gt$sname null ne or $slen 0 gt and{$findfontByEnum} {//SubstituteFont exec}ifelse end}}ifelse bind readonly def}{/findfont{ $SubstituteFont begin dup systemfindfont dup/FontName known{dup/FontName get 2 index ne}{true}ifelse dup{/$used true def}if{$slen 0 gt$sname null ne 3 index length $slen gt or and{pop dup$findfontByEnum findfont dup maxlength 1 add dict begin{1 index/FID eq{pop pop}{def}ifelse}forall currentdict end definefont}{exch pop}ifelse}{exch pop}ifelse end}bind def}ifelse end end}if end %%EndResource %%EndProlog %%BeginSetup Adobe_AGM_Core/AGMCORE_err_strings 3 dict dup begin /AGMCORE_bad_environ (Environment not satisfactory for this job, which requests at least PostScript Level ^\tand at least PostScript version ^. Ensure that the PPD is correct or that the PostScript level requested is supported by this printer. ) def /AGMCORE_color_space_onhost_seps (This job has content that will not separate with on-host methods. ) def /AGMCORE_invalid_color_space (This job contains an invalid color space. ) def end put 2 2010 true Adobe_AGM_Core/doc_setup get exec Adobe_CoolType_Core/doc_setup get exec %%EndSetup %%Page: name:1 1 %%EndPageComments %%BeginPageSetup Adobe_AGM_Core/page_setup get exec Adobe_CoolType_Core/page_setup get exec %%EndPageSetup Adobe_AGM_Core/AGMCORE_save save ddf mark /0 [/DeviceGray] add_csa /CSA /0 /1 [/DeviceCMYK] add_csa /CSA /1 /2 [/DeviceRGB] add_csa /CSA /2 cleartomark 800 path_rez 1 -1 scale 0 -140.785 translate gsave [1 0 0 1 0 0 ] concat gsave 0 0 mo 0 140.785 ln 229.617 140.785 ln 229.617 0 ln clp 0.25 lw 1 lc 1 lj 10 ml [] 0 dsh true sadj 53.8984 129.717 mo 53.8984 128.374 ln false op 0 0 0 1 cmyk s save_ctm restore_ctm 87.9941 129.717 mo 87.9941 128.374 ln s save_ctm %%IncludeResource: font Courier /Courier*1 [ 46{/.notdef}repeat /period /.notdef /zero 4{/.notdef}repeat /five 202{/.notdef}repeat ] /Courier nfnt /Courier*1 findfont [10 0 0 -10 0 0 ]mfnt sfnt BuildWidthShowArray 44.7207 138.295 mov (0.5) sh restore_ctm 122.089 129.717 mo 122.089 128.374 ln s save_ctm %%IncludeResource: font Courier /Courier*2 [ 49{/.notdef}repeat /one 206{/.notdef}repeat ] /Courier nfnt /Courier*2 findfont [10 0 0 -10 0 0 ]mfnt sfnt BuildWidthShowArray 84.8164 138.295 mov (1) sh restore_ctm 156.185 129.717 mo 156.185 128.374 ln s save_ctm /Courier*2 findfont [10 0 0 -10 0 0 ]mfnt sfnt BuildWidthShowArray 112.947 138.295 mov (1) sh /Courier*1 findfont [10 0 0 -10 0 0 ]mfnt sfnt BuildWidthShowArray 118.947 138.295 mov (.5) sh restore_ctm 190.281 129.717 mo 190.281 128.374 ln s save_ctm %%IncludeResource: font /Courier*3 [ 50{/.notdef}repeat /two ] /Courier nfnt /Courier*3 findfont [10 BuildWidthShowArray 153.302 138.295 mov (2) sh restore_ctm 224.376 129.717 mo 224.376 128.374 ln s save_ctm /Courier*3 findfont [10 BuildWidthShowArray 181.289 138.295 mov (2) sh /Courier*1 findfont [10 BuildWidthShowArray 187.288 138.295 mov (.5) sh restore_ctm 0.125 lw 26.623 129.717 mo 26.623 128.911 ln 33.4409 129.717 mo 33.4409 128.911 ln 40.2607 129.717 mo 40.2607 128.911 ln 47.0786 129.717 mo 47.0786 128.911 ln 60.7188 129.717 mo 60.7188 128.911 ln 67.5361 129.717 mo 67.5361 128.911 ln 74.3564 129.717 mo 74.3564 128.911 ln 81.1743 129.717 mo 81.1743 128.911 ln 94.814 129.717 mo 94.814 128.911 ln 101.632 129.717 mo 101.632 128.911 ln 108.452 129.717 mo 108.452 128.911 ln 115.27 129.717 mo 115.27 128.911 ln 128.91 129.717 mo 128.91 128.911 ln 135.728 129.717 mo 135.728 128.911 ln 142.548 129.717 mo 142.548 128.911 ln 149.365 129.717 mo 149.365 128.911 ln 163.005 129.717 mo 163.005 128.911 ln 169.824 129.717 mo Courier 205{/.notdef}repeat 0 0 -10 0 0 ]mfnt sfnt 0 0 -10 0 0 ]mfnt sfnt 0 0 -10 0 0 ]mfnt sfnt 169.824 128.911 ln 176.642 129.717 mo 176.642 128.911 ln 183.46 129.717 mo 183.46 128.911 ln 197.101 129.717 mo 197.101 128.911 ln 203.919 129.717 mo 203.919 128.911 ln 210.738 129.717 mo 210.738 128.911 ln 217.556 129.717 mo 217.556 128.911 ln s 0.25 lw 14.6885 129.717 mo 229.492 129.717 ln 19.8032 99.29 mo 21.1455 99.29 ln s save_ctm %%IncludeResource: font Courier /Courier*4 [ 51{/.notdef}repeat /three 204{/.notdef}repeat ] /Courier nfnt /Courier*4 findfont [10 0 0 -10 0 0 ]mfnt sfnt BuildWidthShowArray 221.494 138.295 mov (3) sh restore_ctm 19.8032 68.8633 mo 21.1455 68.8633 ln s save_ctm /Courier*1 findfont [10 0 0 -10 0 0 ]mfnt sfnt BuildWidthShowArray 0 102.202 mov (0.5) sh restore_ctm 19.8032 38.4365 mo 21.1455 38.4365 ln s save_ctm /Courier*2 findfont [10 0 0 -10 0 0 ]mfnt sfnt BuildWidthShowArray 11.9297 71.8359 mov (1) sh restore_ctm 19.8032 8.00977 mo 21.1455 8.00977 ln s save_ctm /Courier*2 findfont [10 0 0 -10 0 0 ]mfnt sfnt BuildWidthShowArray 0 41.3496 mov (1) sh /Courier*1 findfont [10 0 0 -10 0 0 ]mfnt sfnt BuildWidthShowArray 5.99991 41.3496 mov (.5) sh restore_ctm 0.125 lw 19.8032 123.632 mo 20.6084 123.632 ln 19.8032 117.546 mo 20.6084 117.546 ln 19.8032 111.461 mo 20.6084 111.461 ln 19.8032 105.375 mo 20.6084 105.375 ln 19.8032 93.2051 mo 20.6084 93.2051 ln 19.8032 87.1191 mo 20.6084 87.1191 ln 19.8032 81.0342 mo 20.6084 81.0342 ln 19.8032 74.9482 mo 20.6084 74.9482 ln 19.8032 62.7783 mo 20.6084 62.7783 ln 19.8032 56.6934 mo 20.6084 56.6934 ln 19.8032 50.6074 mo 20.6084 50.6074 ln 19.8032 44.5225 mo 20.6084 44.5225 ln 19.8032 32.3516 mo 20.6084 32.3516 ln 19.8032 26.2666 mo 20.6084 26.2666 ln 19.8032 20.1807 mo 20.6084 20.1807 ln 19.8032 14.0957 mo 20.6084 14.0957 ln 19.8032 1.9248 mo 20.6084 1.9248 ln s 0.25 lw 19.8032 132.879 mo 19.8032 0.125 ln s /Courier*3 findfont [10 0 0 -10 0 0 ]mfnt sfnt BuildWidthShowArray 12.2197 10.9824 mov (2) sh gsave 14.6885 132.879 mo 229.492 132.879 ln 229.492 0.125 ln 14.6885 0.125 ln 14.6885 132.879 ln clp 2.14802 lw 19.8032 129.717 mo 20.0566 129.717 ln 20.2842 129.717 ln 20.5508 129.715 ln 20.8018 129.71 ln 21.2466 129.704 ln 21.7319 129.693 ln 22.2646 129.678 ln 22.8296 129.659 ln 23.8433 129.611 ln 24.8896 129.549 ln 25.8691 129.477 ln 28.1006 129.268 ln 30.3799 128.986 ln 32.4614 128.669 ln 37.1528 127.749 ln 41.2319 126.714 ln 45.6826 125.335 ln 54.4121 121.881 ln 62.8174 117.61 ln 71.751 112.061 ln 80.356 105.726 ln 88.6362 98.7148 ln 97.4453 90.2725 ln 105.926 81.1846 ln 114.084 71.5547 ln 122.767 60.3486 ln 131.125 48.6289 ln 140.009 35.1699 ln 148.566 21.2266 ln 156.8 6.91016 ln 156.8 6.91016 mo 160.468 0.125 ln 0.00784314 0.964706 0.615686 0 cmyk s 19.8032 129.717 mo 20.0566 129.717 ln 20.2842 129.717 ln 20.5508 129.717 ln 20.8018 129.717 ln 21.2466 129.715 ln 21.7319 129.713 ln 22.2646 129.708 ln 22.8296 129.704 ln 23.8433 129.691 ln 24.8896 129.676 ln 25.8691 129.656 ln 28.1006 129.605 ln 30.3799 129.534 ln 32.4614 129.457 ln 37.1528 129.228 ln 41.2319 128.972 ln 45.6826 128.632 ln 54.4121 127.79 ln 62.8174 126.766 ln 71.751 125.459 ln 80.356 124.005 ln 88.6362 122.439 ln 97.4453 120.613 ln 105.926 118.717 ln 114.084 116.783 ln 122.767 114.627 ln 131.125 112.477 ln 140.009 110.131 ln 148.566 107.833 ln 156.8 105.607 ln 165.562 103.24 ln 173.994 100.98 ln 182.103 98.8389 ln 190.74 96.6074 ln 199.048 94.5195 ln 207.886 92.376 ln 216.398 90.3955 ln 224.376 88.6211 ln 0.894118 0 1 0 cmyk s 19.8032 129.717 mo 20.0566 129.717 ln 20.2842 129.717 ln 20.5508 129.717 ln 20.8018 129.715 ln 21.2466 129.71 ln 21.7319 129.706 ln 22.2646 129.697 ln 22.8296 129.688 ln 23.8433 129.665 ln 24.8896 129.633 ln 25.8691 129.597 ln 28.1006 129.493 ln 30.3799 129.352 ln 32.4614 129.195 ln 37.1528 128.737 ln 41.2319 128.224 ln 45.6826 127.547 ln 54.4121 125.861 ln 62.8174 123.812 ln 71.751 121.202 ln 80.356 118.294 ln 88.6362 115.162 ln 97.4453 111.51 ln 105.926 107.717 ln 114.084 103.851 ln 122.767 99.5371 ln 131.125 95.2344 ln 140.009 90.543 ln 148.566 85.9492 ln 156.8 81.4961 ln 165.562 76.7637 ln 173.994 72.2422 ln 182.103 67.9609 ln 190.74 63.498 ln 199.048 59.3223 ln 207.886 55.0342 ln 216.398 51.0732 ln 224.376 47.5234 ln 0.333333 0.937255 0.956863 0.25098 cmyk s 19.8032 129.717 mo 28.1006 126.766 ln 37.1528 123.559 ln 45.6523 120.57 ln 53.8276 117.729 ln 62.5293 114.752 ln 70.9043 111.942 ln 79.8081 109.025 ln 88.3853 106.293 ln 96.6357 103.745 ln 105.415 101.127 ln 113.867 98.7061 ln 121.994 96.4717 ln 130.648 94.2012 ln 138.976 92.124 ln 147.832 90.0322 ln 156.359 88.1357 ln 164.564 86.4189 ln 173.294 84.709 ln 181.699 83.1758 ln 190.63 81.666 ln 199.238 80.3213 ln 207.519 79.1309 ln 216.326 77.9668 ln 224.376 76.9961 ln 0.956863 0.929412 0 0 cmyk s grestore grestore grestore Adobe_AGM_Core/AGMCORE_save get restore %%PageTrailer Adobe_CoolType_Core/page_trailer get exec Adobe_AGM_Core/page_trailer get exec %%Trailer Adobe_CoolType_Core/doc_trailer get exec Adobe_AGM_Core/doc_trailer get exec %%EOF gsave userdict /annotatepage 2 copy known {get exec}{pop pop} ifelse grestore 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Fc(\032)2233 3557 y(Z)2349 3692 y Fi(Y)21 b(dQ)h Fk(+)2675 3557 y Fc(Z)2792 3692 y Fi(Y)2870 3651 y Ff(2)2909 3692 y Fi(dQ)3037 3552 y Fc(\033)3145 3692 y Fi(:)304 3927 y Fk(But)33 b(w)m(e)g(also)f(ha)m(v)m (e)811 3997 y Fc(Z)927 4133 y Fi(Y)21 b(dQ)28 b Fk(=)1264 3997 y Fc(Z)1380 4066 y Fh(p)p 1463 4066 96 4 v 67 x Fi(pq)t(d\026)22 b Fh(\000)g Fk(1)28 b(=)f Fh(\000)p Fi(H)2136 4092 y Ff(2)2176 4133 y Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)g Fi(;)811 4252 y Fc(Z)927 4388 y Fi(Y)1005 4346 y Ff(2)1044 4388 y Fi(dQ)28 b Fk(=)1304 4252 y Fc(Z)1403 4388 y Fk([)1430 4298 y Fc(p)p 1530 4298 145 4 v 90 x Fi(p=q)e Fh(\000)c Fk(1])1872 4346 y Ff(2)1912 4388 y Fi(q)t(d\026)27 b Fk(=)2199 4252 y Fc(Z)2299 4388 y Fk([)2326 4321 y Fh(p)p 2409 4321 49 4 v 67 x Fi(p)22 b Fh(\000)2580 4321 y(p)p 2663 4321 47 4 v 67 x Fi(q)s Fk(])2736 4346 y Ff(2)2776 4388 y Fi(d\026)27 b Fk(=)h(2)p Fi(H)3155 4346 y Ff(2)3193 4388 y Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)g Fi(:)304 4613 y Fk(By)33 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Fh(\000)i Fi(\032)p Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)3290 5120 y Fg(n)3337 5161 y Fh(g)304 5344 y Fk(in)34 b(general.)49 b(F)-8 b(or)34 b(the)h(particular)e(case)j(w)m (e)g(b)s(egan)e(with)h Fi(\032)p Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)31 b(=)g(exp)q($$)p Fh(\000)p Fi(\022)3228 5308 y Ff(2)3268 5344 y Fi(=)p Fk(8$$,)k(and)g(th)m(us)304 5464 y(w)m(e)e(conclude)h(that)e(in)g(this)g(case)1240 5647 y Fi(K)7 b Fk($$)p Fi(P)1445 5606 y Fg(n)1491 5647 y Fi(;)17 b(Q)1612 5606 y Fg(n)1659 5647 y Fk($$)28 b Fh(\025)g Fk(2)p Fh(f)p Fk(1)21 b Fh(\000)i Fk(exp)q($$)p Fh(\000)p Fi(n\022)2469 5606 y Ff(2)2509 5647 y Fi(=)p Fk(8$$)p Fh(g)17 b Fi(:)1926 5896 y Fk(3)p eop %%Page: 4 4 4 3 bop 179 297 a Fk(4.)49 b($$33)32 b(p)s(oin)m(ts$$.)43 b(Pro)m(v)m(e)34 b(that:)304 418 y($$a$$)e Fi(d)512 433 y Fg(T)10 b(V)624 418 y Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)27 b Fh(\021)h Fk(sup)1166 441 y Fg(A)p Fd(2A)1343 418 y Fh(j)p Fi(P)14 b Fk($$)p Fi(A)p Fk($$)21 b Fh(\000)i Fi(Q)p Fk($$)p Fi(A)p Fk($$)p Fh(j)k Fk(=)h($$1)p 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Fk(so)d(that)f Fi(\016)g Fk(=)27 b Fi(\016)2101 952 y Ff(+)2182 988 y Fh(\000)c Fi(\016)2329 952 y Fd(\000)2420 988 y Fk(and)33 b Fh(j)p Fi(\016)t Fh(j)27 b Fk(=)h Fi(\016)2891 952 y Ff(+)2972 988 y Fk(+)22 b Fi(\016)3117 952 y Fd(\000)3176 988 y Fk(.)43 b(Noting)32 b(that)591 1252 y(0)27 b(=)771 1116 y Fc(Z)871 1252 y Fk($$)p Fi(p)22 b Fh(\000)g Fi(q)t Fk($$)p Fi(d\026)27 b Fk(=)1405 1116 y Fc(Z)1521 1252 y Fi(\016)t(d\026)g Fk(=)1808 1116 y Fc(Z)1908 1252 y Fk($$)p Fi(\016)1993 1211 y Ff(+)2074 1252 y Fh(\000)c Fi(\016)2221 1211 y Fd(\000)2280 1252 y Fk($$)p Fi(d\026)k Fk(=)2558 1116 y Fc(Z)2674 1252 y Fi(\016)2721 1211 y Ff(+)2780 1252 y Fi(d\026)22 b Fh(\000)3012 1116 y Fc(Z)3128 1252 y Fi(\016)3175 1211 y Fd(\000)3234 1252 y Fi(d\026)17 b(;)304 1521 y Fk(it)31 b(follo)m(ws)h(that)933 1440 y Fc(R)1016 1521 y Fi(\016)1063 1485 y Ff(+)1122 1521 y Fi(d\026)27 b Fk(=)1363 1440 y Fc(R)1446 1521 y Fi(\016)1493 1485 y Fd(\000)1552 1521 y Fi(d\026)32 b Fk(and,)g(moreo)m(v)m(er,)h 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Fi(d\026)g Fk(=)2674 2497 y(1)p 2674 2541 49 4 v 2674 2633 a(2)2750 2429 y Fc(Z)2866 2564 y Fh(j)p Fi(p)22 b Fh(\000)g Fi(q)t Fh(j)p Fi(d\026)17 b(:)304 2832 y Fk(Noting)31 b(that)i(equalit)m(y)f(holds)g(when)i Fi(A)28 b Fk(=)f Fh(f)p Fi(x)h Fk(:)60 b Fi(p)p Fk($$)p Fi(x)p Fk($$)28 b Fh(\025)h Fi(q)t Fk($$)p Fi(x)p Fk($$)p Fh(g)p Fk(,)j(the)h(result)g(follo)m(ws.)304 2952 y($$b$$)65 b(Note)33 b(that)504 3216 y Fi(H)593 3175 y Ff(2)632 3216 y Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)83 b(=)1148 3148 y(1)p 1148 3193 V 1148 3284 a(2)1223 3080 y Fc(Z)1323 3216 y Fk([)1350 3149 y Fh(p)p 1433 3149 V 67 x Fi(p)22 b Fh(\000)1604 3149 y(p)p 1687 3149 47 4 v 67 x Fi(q)s Fk(])1760 3175 y Ff(2)1800 3216 y Fi(d\026)27 b Fk(=)2051 3148 y(1)p 2051 3193 49 4 v 2051 3284 a(2)2126 3080 y Fc(Z)2242 3216 y Fh(j)2270 3149 y(p)p 2353 3149 V 67 x Fi(p)22 b Fh(\000)2524 3149 y(p)p 2607 3149 47 4 v 67 x Fi(q)s Fh(jj)2709 3149 y(p)p 2792 3149 49 4 v 67 x Fi(p)g Fh(\000)2963 3149 y(p)p 3046 3149 47 4 v 67 x Fi(q)s Fh(j)p 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Fk($$)g Fh(\001)g(\001)g(\001)d Fi(p)p Fk($$)p Fi(x)2192 4012 y Fg(n)2240 3997 y Fk($$)p Fi(q)t Fk($$)p Fi(x)2418 4012 y Ff(1)2457 3997 y Fk($$)j Fh(\001)g(\001)g (\001)e Fi(q)t Fk($$)p Fi(x)2785 4012 y Fg(n)2832 3997 y Fk($$)p Fi(d\026)p Fk($$)p Fi(x)3073 4012 y Ff(1)3112 3997 y Fk($$)i Fh(\001)g(\001)g(\001)d Fi(d\026)p Fk($$)p Fi(x)3502 4012 y Fg(n)3549 3997 y Fk($$)1057 4252 y(=)1216 4116 y Fc(Z)1333 4252 y Fh(\001)j(\001)g(\001)1465 4116 y Fc(Z)1582 4162 y(p)p 1681 4162 438 4 v 1681 4252 a Fi(p)p Fk($$)p Fi(x)1823 4267 y Ff(1)1863 4252 y Fk($$)p Fi(q)t Fk($$)p Fi(x)2041 4267 y Ff(1)2081 4252 y Fk($$)f Fh(\001)h(\001)g(\001)2268 4162 y Fc(p)p 2368 4162 453 4 v 90 x Fi(p)p Fk($$)p Fi(x)2510 4267 y Fg(n)2557 4252 y Fk($$)p Fi(q)t Fk($$)p Fi(x)2735 4267 y Fg(n)2782 4252 y Fk($$)p Fi(d\026)p Fk($$)p Fi(x)3023 4267 y Ff(1)3062 4252 y Fk($$)g Fh(\001)g(\001)g(\001)e Fi(d\026)p Fk($$)p Fi(x)3453 4267 y Fg(n)3499 4252 y Fk($$)1057 4507 y(=)1216 4371 y Fc(Z)1333 4416 y(p)p 1432 4416 438 4 v 1432 4507 a Fi(p)p Fk($$)p Fi(x)1574 4522 y Ff(1)1614 4507 y Fk($$)p Fi(q)t Fk($$)p Fi(x)1792 4522 y Ff(1)1832 4507 y Fk($$)o Fi(d\026)p Fk($$)p Fi(x)2072 4522 y Ff(1)2112 4507 y Fk($$)i Fh(\001)g(\001)g(\001)2299 4371 y Fc(Z)2415 4416 y(p)p 2515 4416 453 4 v 91 x Fi(p)p Fk($$)p Fi(x)2657 4522 y Fg(n)2704 4507 y Fk($$)p Fi(q)t Fk($$)p Fi(x)2882 4522 y Fg(n)2929 4507 y Fk($$)p Fi(d\026)p Fk($$)p Fi(x)3170 4522 y Fg(n)3217 4507 y Fk($$)1057 4700 y(=)83 b Fi(\032)p Fk($$)p Fi(P)s(;)17 b(Q)p Fk($$)1529 4659 y Fg(n)1593 4700 y Fi(:)179 5166 y Fk(5.)49 b($$54)32 b(p)s(oin)m(ts$$)304 5286 y(Supp)s(ose)58 b(that)e Fi(X)r(;)17 b(X)1154 5301 y Ff(1)1194 5286 y Fi(;)g(:)g(:)g(:)f(;)h(X)1494 5301 y Fg(n)1597 5286 y Fk(are)57 b(i.i.d.)115 b(with)57 b(distribution)e (function)h Fi(F)3362 5301 y Fg(\022)3458 5286 y Fk(giv)m(en)h(b)m(y) 304 5406 y Fi(F)367 5421 y Fg(\022)406 5406 y Fk($$)p Fi(x)p Fk($$)46 b(=)f Fi(G)p Fk($$)p Fi(x)30 b Fh(\000)g Fi(\022)s Fk($$)43 b(for)f Fi(\022)49 b Fh(2)d Fi(R)e 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Ff(:1)2911 288 y Fh(!)3011 303 y Fg(p)3078 288 y Fi(\022)s Fk(.)304 408 y($$d$$)e(Sho)m(w)g(that)g Fi(n)p Fk($$)p Fi(X)1104 423 y Fg(n)p Ff(:1)1222 408 y Fh(\000)16 b Fi(\022)s Fk($$)29 b Fh(!)1530 423 y Fg(d)1600 408 y Fk(\\something")f(and)i(\014nd)g(the)g(limiting)25 b(disribution.)41 b([Hin)m(t:)304 528 y(Start)32 b(b)m(y)i(computing)d Fi(P)14 b Fk($$)p Fi(n)p Fk(\()p Fi(X)1463 543 y Fg(n)p Ff(:1)1586 528 y Fh(\000)23 b Fi(\022)s Fk($$)28 b Fi(>)f(t)p Fk(\).])304 649 y($$e$$)34 b(Sho)m(w)i(that)e Fi(F)1007 607 y Fd(\000)p Ff(1)993 676 y Fg(\022)1101 649 y Fk($$)p Fi(t)p Fk($$)d(=)f Fi(\022)d Fk(+)c Fi(G)1597 613 y Fd(\000)p Ff(1)1691 649 y Fk($$)p Fi(t)p Fk($$)35 b(for)e Fi(t)e Fh(2)g Fk($$0)p Fi(;)17 b Fk(1$$,)34 b(and)h(use)g(this)f(to)g(\014nd)h (an)f(estimator)312 754 y(^)304 780 y Fi(\022)349 795 y Fg(n)396 780 y Fk($$)p Fi(t)p Fk($$)f(of)f Fi(\022)k Fk(based)d(on)g(the)g Fi(t)p Fh(\000)p Fk(th)g(sample)f(quan)m(tile)g Fe(F)2299 744 y Fd(\000)p Ff(1)2299 805 y Fg(n)2399 780 y Fk($$)p Fi(t)p Fk($$.)304 901 y($$f)7 b($$)32 b(Sho)m(w)h(that)g(the) g(estimators)1566 874 y(^)1558 901 y Fi(\022)1603 916 y Fg(n)1651 901 y Fk($$)p Fi(t)p Fk($$)f(of)h Fi(\022)i Fk(whic)m(h)e(y)m(ou)h(deriv)m(ed)f(in)f($$e$$)h(satisfy)1492 1040 y Fh(p)p 1575 1040 59 4 v 77 x Fi(n)p Fk($$)1679 1090 y(^)1671 1117 y Fi(\022)1716 1132 y Fg(n)1763 1117 y Fk(\()p Fi(t)p Fk($$)22 b Fh(\000)h Fi(\022)s Fk(\))28 b Fh(!)2210 1132 y Fg(d)2278 1117 y Fi(N)10 b Fk($$0)p Fi(;)17 b(V)2575 1075 y Ff(2)2554 1141 y Fg(t)2614 1117 y Fk($$)304 1333 y(and)33 b(compute)f Fi(V)968 1296 y Ff(2)946 1357 y Fg(t)1040 1333 y Fk(explicitly)-8 b(.)304 1453 y($$g$$)43 b(Find)f Fi(t)j Fh(2)h Fk($$0)p Fi(;)17 b Fk(1$$)42 b(whic)m(h)i(minimizes)c(the)k(v)-5 b(ariance)42 b Fi(V)2572 1417 y Ff(2)2550 1478 y Fg(t)2654 1453 y Fk(of)h(the)g(estimator)f(whic)m(h)h(y)m(ou)304 1573 y(found)33 b(in)e($$f)7 b($$.)304 1783 y Fl(Solution:)42 b Fk($$a$$)65 b(No)m(w)726 2048 y Fi(E)6 b Fh(j)p Fi(X)i Fh(j)949 2007 y Fg(r)1070 2048 y Fk(=)1228 1912 y Fc(Z)1345 2048 y Fh(j)p Fi(x)p Fh(j)1456 2007 y Fg(r)1493 2048 y Fi(dF)1607 2063 y Fg(\022)1646 2048 y Fk($$)p Fi(x)p Fk($$)28 b(=)1909 1912 y Fc(Z)2025 2048 y Fh(j)p Fi(x)p Fh(j)2136 2007 y Fg(r)2174 2048 y Fi(dG)p Fk($$)p Fi(x)22 b Fh(\000)h Fi(\022)s Fk($$)k(=)2734 1912 y Fc(Z)2850 2048 y Fh(j)p Fi(y)e Fk(+)d Fi(\022)s Fh(j)3125 2007 y Fg(r)3163 2048 y Fi(dG)p Fk($$)p Fi(y)t Fk($$)1070 2309 y(=)1228 2173 y Fc(Z)1328 2199 y Fd(1)1284 2399 y Ff(0)1419 2309 y Fh(j)p Fi(y)j Fk(+)d Fi(\022)s Fh(j)1694 2268 y Fg(r)1861 2241 y Fk(7)p Fi(=)p Fk(2)p 1742 2286 385 4 v 1742 2377 a([1)g(+)g Fi(y)t Fk(])2017 2348 y Ff(9)p Fg(=)p Ff(2)2136 2309 y Fi(dy)304 2581 y Fk(and)33 b(this)f(in)m(tegral)f(con)m(v)m(erges)k(if)c(9)p Fi(=)p Fk(2)21 b Fh(\000)i Fi(r)30 b(>)e Fk(1,)k(or)h(equiv)-5 b(alen)m(tly)32 b(if)f Fi(r)f(<)e Fk(7)p Fi(=)p Fk(2.)304 2701 y($$b$$)65 b(Di\013eren)m(tiating)30 b Fi(G)i Fk(yields)1416 2961 y Fi(g)t Fk($$)p Fi(x)p Fk($$)c(=)1944 2894 y(7)p 1739 2938 460 4 v 1739 3030 a(2$$1)22 b(+)g Fi(x)p Fk($$)2088 3001 y Ff(9)p Fg(=)p Ff(2)2208 2961 y Fi(;)212 b(x)28 b Fh(\025)g Fk(0)17 b Fi(:)304 3228 y Fk(Both)32 b Fi(G)h Fk(and)g Fi(g)i Fk(are)e(sho)m(wn)h(in)e(the)h(follo)m(wing)c (\014gure:)304 3389 y($$c$$)75 b(Let)38 b Fi(\017)e(>)g Fk(0,)j(and)e(note)h(that)f Fi(X)1693 3404 y Fg(i)1747 3389 y Fh(\000)26 b Fi(\022)39 b Fh(\021)e Fi(Y)2105 3404 y Fg(i)2170 3389 y Fk(are)g(i.i.d.)57 b(with)37 b(distribution)f(function)h Fi(G)p Fk(.)304 3509 y(No)m(w)c Fi(P)14 b Fk($$)p Fi(X)722 3524 y Fg(n)p Ff(:1)851 3509 y Fi(<)27 b(\022)f Fh(\000)c Fi(\017)p Fk($$)28 b(=)g(0)k(for)g(all)f Fi(n)p Fk(,)i(and,)f(on)h(the)g(other)g(hand,)839 3725 y Fi(P)902 3740 y Fg(\022)941 3725 y Fk($$)p Fi(X)1060 3740 y Fg(n)p Ff(:1)1189 3725 y Fi(>)28 b(\022)d Fk(+)d Fi(\017)p Fk($$)84 b(=)f Fi(P)14 b Fk($$)p Fi(X)1977 3740 y Fg(n)p Ff(:1)2100 3725 y Fh(\000)23 b Fi(\022)30 b(>)e(\017)p Fk($$)1622 3871 y(=)83 b Fi(P)14 b Fk($$)p Fi(Y)1953 3886 y Fg(n)p Ff(:1)2081 3871 y 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a(\021)1798 1104 y Fh(\000)1909 1036 y Fk(1)22 b Fh(\000)g Fi(z)p 1908 1081 223 4 v 1908 1172 a Fk(1)g Fh(\000)g Fi(\021)2157 1104 y(:)304 1354 y Fk($$b$$)65 b(Calculating)30 b(second)k(deriv)-5 b(ativ)m(es,)33 b(w)m(e)g(\014nd:)1034 1529 y(\177)1035 1555 y Fi(l)1064 1570 y Fg(\015)t(\015)1149 1555 y Fk($$)p Fi(y)t(;)17 b(z)t Fk($$)82 b(=)h Fh(\000)p Fi(\025z)1794 1514 y Ff(2)1835 1555 y Fi(e)1880 1514 y Fg(\015)t(z)1960 1555 y Fi(y)20 b(;)1033 1674 y Fk(\177)1034 1700 y Fi(l)1063 1715 y Fg(\015)t(\025)1149 1700 y Fk($$)p Fi(y)t(;)d(z)t Fk($$)82 b(=)h Fh(\000)p Fi(z)t(e)1782 1659 y Fg(\015)t(z)1864 1700 y Fi(y)30 b Fk(=)2056 1674 y(_)2046 1700 y Fi(l)2075 1715 y Fg(\025\015)2161 1700 y Fk($$)p Fi(y)t(;)17 b(z)t Fk($$)g Fi(;)1037 1819 y Fk(\177)1037 1845 y Fi(l)1066 1860 y Fg(\015)t(\021)1149 1845 y Fk($$)p Fi(y)t(;)g(z)t Fk($$)82 b(=)1610 1819 y(\177)1611 1845 y Fi(l)1640 1860 y Fg(\025\021)1723 1845 y Fk($$)p Fi(y)t(;)17 b(z)t Fk($$)27 b(=)2074 1819 y(\177)2075 1845 y Fi(l)2104 1860 y Fg(\021)r(\015)2186 1845 y Fk($$)p Fi(y)t(;)17 b(z)t Fk($$)27 b(=)2537 1819 y(\177)2538 1845 y Fi(l)2567 1860 y Fg(\021)r(\025)2650 1845 y Fk($$)p Fi(y)t(;)17 b(z)t Fk($$)27 b(=)h(0)17 b Fi(;)1032 1964 y Fk(\177)1033 1991 y Fi(l)1062 2006 y Fg(\025\025)1149 1991 y Fk($$)p Fi(y)t(;)g(z)t Fk($$)82 b(=)h Fh(\000)p Fi(\025)1745 1950 y Fd(\000)p Ff(2)1856 1991 y Fi(;)1039 2154 y Fk(\177)1040 2181 y Fi(l)1069 2196 y Fg(\021)r(\021)1149 2181 y Fk($$)p Fi(y)t(;)17 b(z)t Fk($$)82 b(=)h Fh(\000)1719 2113 y Fi(z)p 1698 2158 92 4 v 1698 2249 a(\021)1750 2220 y Ff(2)1822 2181 y Fh(\000)1990 2113 y Fk(1)22 b Fh(\000)g Fi(z)p 1931 2158 338 4 v 1931 2249 a Fk($$1)g Fh(\000)h Fi(\021)t Fk($$)2230 2220 y Ff(2)2295 2181 y Fi(:)304 2431 y Fk(Th)m(us,)43 b(computing)c(the)i(exp)s(ectations)f(of)g(these)h(second)h(deriv)-5 b(ativ)m(es,)42 b(and)e(using)g(the)g(fact)304 2552 y(that)j($$)p Fi(\025e)666 2516 y Fg(\015)t(Z)762 2552 y Fi(Y)22 b Fh(j)p Fi(Z)7 b Fk($$)44 b Fh(\030)86 b Fk(Exp)s(onen)m(tial$$1$$,)45 b(w)m(e)f(\014nd)f(that)g(the)g(information)d(matrix)h(for)h Fi(\022)k Fk(is)304 2672 y(giv)m(en)33 b(b)m(y)1082 2905 y Fi(I)8 b Fk($$)p Fi(\022)s Fk($$)27 b(=)1388 2705 y Fc(0)1388 2884 y(@)1550 2784 y Fi(E)6 b Fk($$)p Fi(Z)1740 2748 y Ff(2)1779 2784 y Fk($$)116 b Fi(E)6 b Fk($$)p Fi(Z)h Fk($$)p Fi(=\025)320 b Fk(0)1517 2904 y Fi(E)6 b Fk($$)p Fi(Z)h Fk($$)p Fi(=\025)152 b Fk(1)p Fi(=\025)2158 2868 y Ff(2)2587 2904 y Fk(0)1659 3025 y(0)368 b(0)225 b(1)p Fi(=)p Fk($$)p Fi(\021)t Fk(\(1)21 b Fh(\000)h Fi(\021)t Fk($$\))2915 2705 y Fc(1)2915 2884 y(A)3035 2905 y Fi(:)304 3194 y Fk($$c$$)69 b(Th)m(us)36 b(the)f(information)d (for)i Fi(\015)39 b Fk(when)d Fi(\025)e Fk(is)g(kno)m(wn)i(is)e Fi(I)2585 3209 y Ff(11)2691 3194 y Fk(=)d Fi(E)6 b Fk($$)p Fi(Z)2988 3158 y Ff(2)3027 3194 y Fk($$.)50 b(The)35 b(information)304 3314 y(for)d Fi(\015)37 b Fk(when)d Fi(\025)f Fk(is)f(unkno)m(wn)i(is)699 3515 y Fi(I)742 3530 y Ff(11)p Fd(\001)p Ff(2)955 3515 y Fk(=)83 b Fi(I)1157 3530 y Ff(11)1254 3515 y Fh(\000)22 b Fi(I)1396 3530 y Ff(12)1471 3515 y Fi(I)1522 3473 y Fd(\000)p Ff(1)1514 3539 y(22)1616 3515 y Fi(I)1659 3530 y Ff(21)955 3718 y Fk(=)83 b Fi(E)6 b Fk($$)p Fi(Z)1304 3677 y Ff(2)1343 3718 y Fk($$)22 b Fh(\000)h Fk($$)p Fi(\025)1598 3677 y Fd(\000)p Ff(1)1692 3718 y Fi(E)6 b Fk(\()p Fi(Z)h Fk($$)p Fi(;)17 b Fk(0\))2068 3577 y Fc(\022)2182 3657 y Fi(\025)2239 3621 y Ff(2)2512 3657 y Fk(0)2205 3777 y(0)107 b Fi(\021)t Fk($$1)22 b Fh(\000)g Fi(\021)t Fk($$)2752 3577 y Fc(\023)2842 3718 y Fk($$)p Fi(\025)2937 3677 y Fd(\000)p Ff(1)3031 3718 y Fi(E)6 b Fk(\()p Fi(Z)h Fk($$)p Fi(;)17 b Fk(0\))3390 3677 y Fg(T)955 3930 y Fk(=)83 b Fi(E)6 b Fk($$)p Fi(Z)1304 3889 y Ff(2)1343 3930 y Fk($$)22 b Fh(\000)h Fk($$)p Fi(E)6 b Fk(\()p Fi(Z)h Fk($$\))1807 3889 y Ff(2)1874 3930 y Fk(=)27 b Fi(V)22 b(ar)s Fk($$)p Fi(Z)7 b Fk($$)17 b Fi(:)304 4131 y Fk(Geometrically)-8 b(,)33 b Fi(I)996 4146 y Ff(11)1105 4131 y Fk(is)i(the)h(squared)g(length)f(of)f(the)i($$ra)m(w$$)f(score) 2847 4105 y(_)2837 4131 y Fi(l)2866 4146 y Fg(\015)2946 4131 y Fk(for)f Fi(\015)j Fk(=)32 b Fi(\022)3338 4146 y Ff(1)3413 4131 y Fk(in)i Fi(L)3595 4146 y Ff(2)3635 4131 y Fk($$)p Fi(P)3736 4146 y Fg(\022)3775 4131 y Fk($$,)304 4251 y(while)e Fi(I)602 4266 y Ff(11)p Fd(\001)p Ff(2)764 4251 y Fk(is)g(the)h(squared)h(length)e(of)g(the)h(e\016cien)m(t)g (score)h(for)e Fi(\015)37 b Fk(giv)m(en)c(b)m(y)1417 4452 y Fi(l)1448 4411 y Fd(\003)1446 4476 y Fg(\015)1518 4452 y Fk(=)1632 4425 y(_)1622 4452 y Fi(l)1651 4467 y Fg(\015)1717 4452 y Fh(\000)23 b Fi(I)1860 4467 y Ff(12)1935 4452 y Fi(I)1986 4411 y Fd(\000)p Ff(1)1978 4476 y(22)2090 4425 y Fk(_)2080 4452 y Fi(l)2109 4467 y Ff(2)2193 4452 y Fk(=)k(\005$$)2417 4425 y(_)2407 4452 y Fi(l)2436 4467 y Fg(\015)2481 4452 y Fh(j)2542 4427 y Fk(_)2509 4452 y Fh(P)2586 4411 y Fd(?)2578 4476 y Ff(2)2645 4452 y Fk($$)17 b Fi(:)304 4652 y Fk($$d$$)65 b(The)33 b(score)h(equations)f (for)f Fi(\022)f Fk(=)c($$)p Fi(\015)5 b(;)17 b(\025;)g(\021)t Fk($$)32 b(are)g(giv)m(en)h(b)m(y)735 4929 y(0)83 b(=)1077 4804 y Fg(n)1026 4834 y Fc(X)1041 5044 y Fg(i)p Ff(=1)1197 4902 y Fk(_)1187 4929 y Fi(l)1216 4944 y Fg(\015)1260 4929 y Fk($$)p Fi(Y)1355 4944 y Fg(i)1383 4929 y Fi(;)17 b(Z)1494 4944 y Fg(i)1522 4929 y Fk($$)27 b(=)1741 4804 y Fg(n)1691 4834 y Fc(X)1706 5044 y Fg(i)p Ff(=1)1851 4929 y Fi(Z)1918 4944 y Fg(i)1946 4929 y Fk($$1)22 b Fh(\000)h Fi(\025e)2257 4887 y Fg(\015)t(Z)2345 4897 y Fa(i)2375 4929 y Fi(Y)2432 4944 y Fg(i)2460 4929 y Fk($$)17 b Fi(;)735 5250 y Fk(0)83 b(=)1077 5126 y Fg(n)1026 5156 y Fc(X)1041 5365 y Fg(i)p Ff(=1)1197 5224 y Fk(_)1187 5250 y Fi(l)1216 5265 y Fg(\025)1261 5250 y Fk($$)p Fi(Y)1356 5265 y Fg(i)1384 5250 y Fi(;)17 b(Z)1495 5265 y Fg(i)1522 5250 y Fk($$)28 b(=)1742 5126 y Fg(n)1692 5156 y Fc(X)1706 5365 y Fg(i)p Ff(=1)1852 5250 y Fi(\025)1909 5209 y Fd(\000)p Ff(1)2003 5250 y Fk($$1)22 b Fh(\000)h Fi(\025e)2314 5209 y Fg(\015)t(Z)2402 5219 y Fa(i)2432 5250 y Fi(Y)2489 5265 y Fg(i)2517 5250 y Fk($$)17 b Fi(;)735 5572 y Fk(0)83 b(=)1077 5447 y Fg(n)1026 5477 y Fc(X)1041 5687 y Fg(i)p Ff(=1)1197 5545 y Fk(_)1187 5572 y Fi(l)1216 5587 y Fg(\021)1258 5572 y Fk($$)p Fi(Y)1353 5587 y Fg(i)1380 5572 y Fi(;)17 b(Z)1491 5587 y Fg(i)1519 5572 y Fk($$)28 b(=)1739 5447 y Fg(n)1688 5477 y Fc(X)1703 5687 y Fg(i)p Ff(=1)1849 5431 y Fc(\032)1933 5504 y Fi(Z)2000 5519 y Fg(i)p 1933 5549 95 4 v 1955 5640 a Fi(\021)2060 5572 y Fh(\000)2170 5504 y Fk(1)22 b Fh(\000)h Fi(Z)2408 5519 y Fg(i)p 2170 5549 266 4 v 2192 5640 a Fk(1)f Fh(\000)g Fi(\021)2445 5431 y Fc(\033)2548 5572 y Fk(=)2793 5504 y(1)p 2661 5549 312 4 v 2661 5640 a Fi(\021)t Fk($$1)g Fh(\000)h Fi(\021)2983 5572 y(n)p Fk(\()p 3079 5492 74 4 v Fi(Z)29 b Fh(\000)23 b Fi(\021)t Fk($$)17 b Fi(:)1926 5896 y Fk(7)p eop %%Page: 8 8 8 7 bop 304 47 a Fk(The)42 b(third)e(equation)h(has)g(the)g(unique)h (solution)h Fc(b)-59 b Fi(\021)46 b Fk(=)p 2444 -33 74 4 v 41 w Fi(Z)7 b Fk(.)69 b(The)42 b(second)g(equation)f(can)g(b)s(e) 304 167 y(solv)m(ed)33 b(for)747 141 y Fc(b)746 167 y Fi(\025)p Fk($$)p Fi(\015)5 b Fk($$)32 b(for)g(eac)m(h)i(\014xed)g(v)-5 b(alue)32 b(of)g Fi(\015)37 b Fk(to)c(obtain)1637 384 y Fc(b)1636 410 y Fi(\025)p Fk($$)p Fi(\015)5 b Fk($$)27 b(=)2181 343 y Fi(n)p 1966 387 489 4 v 1966 404 a Fc(P)2071 430 y Fg(n)2071 508 y(i)p Ff(=1)2206 479 y Fi(Y)2263 494 y Fg(i)2291 479 y Fi(e)2336 450 y Fg(\015)t(Z)2424 460 y Fa(i)2481 410 y Fi(:)304 688 y Fk(Substituting)32 b(this)g(in)m(to)g(the)h(\014rst)g(equation,)f(w)m(e)i(see)f(that)g Fc(b)-55 b Fi(\015)37 b Fk(satis\014es)p 1681 884 74 4 v 1681 964 a Fi(Z)e Fk(=)1897 822 y Fc(P)2002 848 y Fg(n)2002 925 y Ff(1)2065 896 y Fi(Z)2132 911 y Fg(i)2160 896 y Fi(Y)2217 911 y Fg(i)2245 896 y Fi(e)2290 860 y Fg(\015)t(Z)2378 870 y Fa(i)p 1897 941 513 4 v 1944 958 a Fc(P)2049 984 y Fg(n)2049 1062 y Ff(1)2113 1033 y Fi(Y)2170 1048 y Fg(i)2198 1033 y Fi(e)2243 1004 y Fg(\015)t(Z)2331 1014 y Fa(i)2435 964 y Fi(;)304 1239 y Fk(whic)m(h)e(has)g(a)f(unique)h (solution)e(if)h(not)g(all)f Fi(Z)7 b Fk('s)33 b(are)f(either)h(0)f(or) g(1.)304 1359 y($$e$$)h(F)-8 b(rom)31 b(our)h(theory)h(in)f(Chapter)h (4)g(w)m(e)g(kno)m(w)h(that)1479 1514 y Fh(p)p 1562 1514 59 4 v 76 x Fi(n)p Fk($$)1663 1564 y Fc(b)1658 1590 y Fi(\022)26 b Fh(\000)c Fi(\022)s Fk($$)28 b Fh(!)2042 1605 y Fg(d)2110 1590 y Fi(N)2188 1605 y Ff(3)2227 1590 y Fk($$0)p Fi(;)17 b(I)8 b Fk(\()p Fi(\022)s Fk($$)2533 1549 y Fd(\000)p Ff(1)2627 1590 y Fk(\))304 1810 y(where)34 b Fi(I)8 b Fk($$)p Fi(\022)s Fk($$)32 b(w)m(as)i(computed)e(in)g ($$b$$,)h(and)980 1954 y Fh(p)p 1063 1954 V 76 x Fi(n)p Fk($$)p Fc(b)-55 b Fi(\015)27 b Fh(\000)c Fi(\015)5 b Fk($$)28 b Fh(!)1559 2045 y Fg(d)1626 2030 y Fi(N)1704 2045 y Ff(1)1744 2030 y Fk($$0)p Fi(;)17 b Fk(1)p Fi(=I)2016 2045 y Ff(11)p Fd(\001)p Ff(2)2144 2030 y Fk(\()p Fi(\022)s Fk($$\))28 b(=)g Fi(N)2516 2045 y Ff(1)2555 2030 y Fk($$0)p Fi(;)17 b Fk(1)p Fi(=V)k(ar)s Fk(\()p Fi(Z)7 b Fk($$\))304 2250 y(as)33 b(w)m(as)g(computed)g(in)f($$c$$.)1926 5896 y(8)p eop %%Page: 9 9 9 8 bop 179 47 a Fk(7.)49 b($$60)32 b(p)s(oin)m(ts$$.)43 b($$P)m(arametric)32 b(Co)m(x)h(mo)s(del,)e(con)m(tin)m(ued$$.)304 167 y($$a$$)93 b(Suggest)48 b(three)g(tests)g(of)e(the)i($$comp)s (osite!$$)85 b(n)m(ull)46 b(h)m(yp)s(othesis)i Fi(H)60 b Fk(:)52 b Fi(\015)57 b Fk(=)52 b(0)47 b(v)m(ersus)304 288 y Fi(K)i Fk(:)42 b Fi(\015)47 b Fh(6)p Fk(=)42 b(0.)69 b(What)41 b(is)g(the)g(asymptotic)f(distribution)f(of)i(eac)m(h)h(of)e (these)j(three)e(statistics)304 408 y(under)33 b(the)g(n)m(ull)f(h)m (yp)s(othesis)h(and)g(under)g(lo)s(cal)e(alternativ)m(es)h(of)g(the)h (form)e Fi(\015)3204 423 y Fg(n)3279 408 y Fk(=)c Fi(tn)3475 372 y Fd(\000)p Ff(1)p Fg(=)p Ff(2)3641 408 y Fk(?)304 528 y($$b$$)d(If)f(in)g($$a$$)g(w)m(e)i(w)m(ere)g(testing)e(the)i (simple)d(n)m(ull)g(h)m(yp)s(othesis)j Fi(H)2652 543 y Fg(s)2716 528 y Fk(:)j Fi(\022)j Fk(=)c Fi(\022)2995 543 y Ff(0)3059 528 y Fk(v)m(ersus)f Fi(K)3427 543 y Ff(2)3494 528 y Fk(:)i Fi(\022)i Fh(6)p Fk(=)e Fi(\022)3773 543 y Ff(0)3813 528 y Fk(,)304 649 y(brie\015y)35 b(describ)s(e)g(the)g (limiting)c(b)s(eha)m(vior)j(of)g(the)i(three)f(statistics)f(corresp)s (onding)h(to)f(those)304 769 y(in)e($$a$$)g(for)g(a)g(\014xed)i (alternativ)m(e.)304 889 y($$c$$)65 b(Consider)33 b(estimation)e(of)h (the)h(function)916 1144 y Fi(q)t Fk($$)p Fi(\022)s Fk($$)28 b(=)f Fi(\027)6 b Fk($$)p Fi(P)1373 1159 y Fg(\022)1412 1144 y Fk($$)28 b(=)g Fi(P)1645 1159 y Fg(\022)1684 1144 y Fk($$)p Fi(Y)48 b(>)28 b Fk(1)p Fh(j)p Fi(Z)34 b Fk(=)28 b(1$$)f(=)2440 1077 y Fi(P)2503 1092 y Fg(\022)2542 1077 y Fk($$)p Fi(Y)49 b(>)28 b Fk(1)p Fi(;)17 b(Z)34 b Fk(=)27 b(1$$)p 2440 1122 734 4 v 2591 1213 a Fi(P)2654 1228 y Fg(\022)2693 1213 y Fk($$)p Fi(Z)35 b Fk(=)27 b(1$$)3201 1144 y Fi(:)304 1400 y Fk(Compute)33 b Fi(q)t Fk($$)p Fi(\022)s Fk($$)f(explicitly)f(as)h(a)h(function)f(of)g Fi(\022)s Fk(.)304 1521 y($$d$$)43 b(Suggest)i(a)e(natural)f(empirical) f(estimator)h(of)h(this)g($$conditional$$)e(probabilit)m(y)g(whic)m(h) 304 1641 y(do)s(es)33 b(not)f(rely)g(on)g(the)h(exp)s(onen)m(tial)f(mo) s(del.)42 b(If)32 b(this)g(estimator)f(is)h(called)k(~)-54 b Fi(\027)3186 1656 y Fg(n)3233 1641 y Fk(,)32 b(sho)m(w)i(that)j(~)-54 b Fi(\027)3793 1656 y Fg(n)304 1762 y Fk(is)32 b(asymptotically)e (linear)h(and)i(\014nd)g(its)f(in\015uence)i(function)e Fi( )k Fk(explicitly)-8 b(.)304 1882 y($$e$$)47 b(Find)f(the)h (e\016cien)m(t)g(in\015uence)h(function)2088 1856 y(~)2089 1882 y Fi(l)2118 1897 y Fg(\027)2208 1882 y Fk(for)e(estimation)e(of)j Fi(\027)6 b Fk($$)p Fi(P)3143 1897 y Fg(\022)3182 1882 y Fk($$)47 b(assuming)f(the)304 2002 y(P)m(oisson)33 b(mo)s(del.)304 2123 y($$f)7 b($$)32 b(Describ)s(e)h(the)g (relationship)d(b)s(et)m(w)m(een)35 b Fi( )h Fk(and)2211 2096 y(~)2212 2123 y Fi(l)2241 2138 y Fg(\027)2317 2123 y Fk(geometrically)-8 b(.)304 2326 y Fl(Solution:)304 2446 y Fk($$a$$)77 b(Three)40 b(p)s(ossible)e(statistics)g(for)g (testing)g Fi(H)46 b Fk(:)38 b Fi(\015)43 b Fk(=)38 b(0)g(v)m(ersus)j Fi(K)k Fk(:)38 b Fi(\015)43 b Fh(6)p Fk(=)38 b(0)g(are)h(the)g(LR,)304 2567 y(W)-8 b(ald,)32 b(and)g(Rao)g(statistics)g(giv)m(en)h(b)m(y)925 2818 y(2)17 b(log)f Fi(\025)1190 2833 y Fg(n)1320 2818 y Fk(=)83 b(2)17 b(log)1687 2678 y Fc(\022)1787 2751 y Fk(sup)1934 2775 y Fg(\022)r Fd(2)p Ff(\002)2092 2751 y Fi(L)2158 2766 y Fg(n)2205 2751 y Fk($$)p Fi(\022)s Fk($$)p 1770 2796 577 4 v 1770 2887 a(sup)1917 2910 y Fg(\022)r Fd(2)p Ff(\002)2054 2919 y Fb(0)2109 2887 y Fi(L)2175 2902 y Fg(n)2222 2887 y Fk($$)p Fi(\022)s Fk($$)2356 2678 y Fc(\023)1098 3047 y Fi(W)1190 3062 y Fg(n)1320 3047 y Fk(=)83 b([)p Fi(n)1564 3006 y Ff(1)p Fg(=)p Ff(2)1674 3047 y Fk($$)p Fc(b)-55 b Fi(\015)27 b Fh(\000)c Fk(0$$])2016 3022 y(^)2004 3047 y Fi(I)2047 3062 y Ff(11)p Fd(\001)p Ff(2)2176 3047 y Fk([)p Fi(n)2261 3006 y Ff(1)p Fg(=)p Ff(2)2372 3047 y Fk($$)p Fc(b)-55 b Fi(\015)27 b Fh(\000)22 b Fk(0$$])28 b(=)f Fi(n)p Fc(b)-55 b Fi(\015)2946 3006 y Ff(2)2998 3022 y Fk(^)2986 3047 y Fi(I)3029 3062 y Ff(11)p Fd(\001)p Ff(2)3175 3047 y Fi(;)1116 3203 y(R)1190 3218 y Fg(n)1320 3203 y Fk(=)83 b([)p Fi(Z)1573 3218 y Fg(n)1620 3203 y Fk($$)1663 3177 y Fc(b)1658 3203 y Fi(\022)1706 3162 y Ff(0)1703 3228 y Fg(n)1750 3203 y Fk($$])1815 3162 y Fg(T)1882 3178 y Fk(^)1870 3203 y Fi(I)8 b Fk($$)1964 3177 y Fc(b)1959 3203 y Fi(\022)2007 3162 y Ff(0)2004 3228 y Fg(n)2051 3203 y Fk($$)2089 3162 y Fd(\000)p Ff(1)2183 3203 y Fk([)p Fi(Z)2277 3218 y Fg(n)2324 3203 y Fk($$)2367 3177 y Fc(b)2362 3203 y Fi(\022)2410 3162 y Ff(0)2407 3228 y Fg(n)2455 3203 y Fk($$])17 b Fi(:)304 3404 y Fk(All)34 b(three)j(of)e(these)i(test)f(statistics)g (con)m(v)m(erge)h(in)e(distribution)f(under)j(the)f(n)m(ull)f(h)m(yp)s (othesis)304 3524 y(to)h Fi(\037)488 3488 y Ff(2)488 3549 y(1)527 3524 y Fk(.)54 b(The)37 b(Rao)e(statistic)h(is)f(the)i (easiest)f(to)g(calculate,)g(it)f(simply)g(en)m(tails)g(calculation)e (of)308 3629 y Fc(b)304 3655 y Fi(\022)352 3619 y Ff(0)349 3680 y Fg(n)434 3655 y Fk(=)k($$0)p Fi(;)679 3629 y Fc(b)678 3655 y Fi(\025)735 3619 y Ff(0)774 3655 y Fi(;)20 b Fc(b)-58 b Fi(\021)870 3619 y Ff(0)909 3655 y Fk($$,)40 b(and)e(this)g(is)g (easy)i(b)s(ecause)f(the)g(score)h(equation)e(for)g Fi(\025)g Fk(has)h(the)f(explicit)304 3787 y(solution)674 3760 y Fc(b)673 3787 y Fi(\025)730 3750 y Ff(0)730 3811 y Fg(n)804 3787 y Fk(=)28 b(1)p Fi(=)p 1006 3707 79 4 v(Y)1084 3802 y Fg(n)1163 3787 y Fk(while)36 b Fc(b)-59 b Fi(\021)1470 3750 y Ff(0)1537 3787 y Fk(=)31 b Fc(b)-59 b Fi(\021)32 b Fk(=)p 1823 3707 74 4 v 27 w Fi(Z)7 b Fk(.)304 3907 y($$b$$)69 b(If)34 b(w)m(e)i(w)m(ere)f(testing)f(a)h(simple)e(n)m(ull)g (h)m(yp)s(othesis)i Fi(H)2443 3922 y Fg(s)2511 3907 y Fk(:)c Fi(\022)j Fk(=)c Fi(\022)2799 3922 y Ff(0)2874 3907 y Fk(v)m(ersus)36 b Fi(K)3252 3922 y Fg(s)3320 3907 y Fk(:)31 b Fi(\022)j Fh(6)p Fk(=)d Fi(\022)3609 3922 y Ff(0)3683 3907 y Fk(and)304 4027 y Fi(\022)g Fh(6)p Fk(=)c Fi(\022)528 4042 y Ff(0)601 4027 y Fk(is)32 b(true,)h(then)1288 4227 y Fi(n)1346 4186 y Fd(\000)p Ff(1)1441 4227 y Fk(2)17 b(log)f Fi(\025)1706 4242 y Fg(n)1780 4227 y Fh(!)1880 4242 y Fg(p)1947 4227 y Fk(2)p Fi(K)7 b Fk($$)p Fi(P)2187 4242 y Fg(\022)2226 4227 y Fi(;)17 b(P)2333 4242 y Fg(\022)2366 4251 y Fb(0)2404 4227 y Fk($$)g Fi(;)1288 4373 y(W)1380 4388 y Fg(n)1455 4373 y Fh(!)1555 4388 y Fg(p)1622 4373 y Fk($$)p Fi(\022)25 b Fh(\000)e Fi(\022)1875 4388 y Ff(0)1915 4373 y Fk($$)1953 4332 y Fg(T)2008 4373 y Fi(I)8 b Fk($$)p Fi(\022)s Fk($$$$)p Fi(\022)25 b Fh(\000)d Fi(\022)2435 4388 y Ff(0)2475 4373 y Fk($$)17 b Fi(;)1288 4518 y(R)1362 4533 y Fg(n)1437 4518 y Fh(!)1537 4533 y Fg(p)1604 4518 y Fi(E)1676 4533 y Fg(\022)1717 4492 y Fk(_)1715 4518 y Fl(l)1747 4533 y Fg(\022)1785 4518 y Fk($$)p Fi(\022)1868 4533 y Ff(0)1908 4518 y Fh(j)p Fi(X)2017 4533 y Ff(1)2056 4518 y Fk($$)2094 4477 y Fg(T)2149 4518 y Fi(I)2200 4477 y Fd(\000)p Ff(1)2295 4518 y Fk($$)p Fi(\022)2378 4533 y Ff(0)2417 4518 y Fk($$)p Fi(E)2527 4533 y 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Fi(:)1926 5896 y Fk(9)p eop %%Page: 10 10 10 9 bop 304 47 a Fk(Th)m(us)34 b(a)e(natural)g(nonparametric)f (estimator)g(of)h Fi(\027)6 b Fk($$)p Fi(P)2324 62 y Fg(\022)2364 47 y Fk($$)32 b(is)744 327 y Fc(b)-57 b Fi(\027)34 b Fh(\021)28 b Fi(\027)6 b Fk($$)p Fe(P)1080 342 y Fg(n)1129 327 y Fk($$)28 b(=)1308 259 y Fe(P)1367 274 y Fg(n)1416 259 y Fk($$)p Fi(Y)49 b Fh(\025)28 b Fi(y)1713 274 y Ff(0)1752 259 y Fi(;)17 b(Z)35 b Fk(=)27 b(1$$)p 1308 304 780 4 v 1479 395 a Fe(P)1538 410 y Fg(n)1587 395 y Fk($$)p Fi(Z)35 b Fk(=)27 b(1$$)2125 327 y(=)2239 259 y Fi(n)2297 222 y Fd(\000)p Ff(1)2408 184 y Fc(P)2513 210 y Fg(n)2513 288 y Ff(1)2577 259 y Fk(1)p Fh(f)p Fi(Y)2733 274 y Fg(i)2788 259 y Fh(\025)h Fi(y)2941 274 y Ff(0)2980 259 y Fi(;)17 b(Z)3091 274 y Fg(i)3146 259 y Fk(=)28 b(1)p Fh(g)p 2239 304 1110 4 v 2413 395 a Fi(n)2471 366 y Fd(\000)p Ff(1)2582 320 y Fc(P)2687 346 y Fg(n)2687 424 y Ff(1)2751 395 y Fk(1)p Fh(f)p Fi(Z)2917 410 y Fg(i)2972 395 y Fk(=)g(1)p Fh(g)3375 327 y Fi(:)304 607 y Fk($$b$$)65 b(T)-8 b(o)33 b(sho)m(w)g(that)i Fc(b)-57 b Fi(\027)39 b Fk(is)32 b(asymptotically)e(linear,)h(w)m(e)j(write)304 807 y Fh(p)p 387 807 59 4 v 77 x Fi(n)p Fk($$)r Fc(b)-57 b Fi(\027)29 b Fh(\000)22 b Fi(\027)6 b Fk(\()p Fi(P)814 899 y Fg(\022)854 884 y Fk($$\))83 b(=)1171 807 y Fh(p)p 1254 807 V 77 x Fi(n)1329 743 y Fc(\032)1414 816 y Fe(P)1473 831 y Fg(n)1522 816 y Fk($$)p Fi(Y)49 b Fh(\025)28 b Fi(y)1819 831 y Ff(0)1858 816 y Fi(;)17 b(Z)34 b Fk(=)28 b(1$$)22 b Fh(\000)g Fi(P)14 b Fk($$)p Fi(Y)49 b Fh(\025)28 b Fi(y)2689 831 y Ff(0)2728 816 y Fi(;)17 b(Z)34 b Fk(=)28 b(1$$)p 1414 861 1650 4 v 2020 952 a Fe(P)2079 967 y Fg(n)2128 952 y Fk($$)p Fi(Z)34 b Fk(=)28 b(1$$)1376 1156 y(+)33 b Fi(P)14 b Fk($$)p Fi(Y)48 b Fh(\025)28 b Fi(y)1858 1171 y Ff(0)1897 1156 y Fi(;)17 b(Z)35 b Fk(=)27 b(1$$)2250 1016 y Fc(\022)2527 1089 y Fk(1)p 2333 1133 438 4 v 2333 1225 a Fe(P)2392 1240 y Fg(n)2441 1225 y Fk($$)p Fi(Z)34 b Fk(=)28 b(1$$)2803 1156 y Fh(\000)3091 1089 y Fk(1)p 2912 1133 407 4 v 2912 1225 a Fi(P)14 b Fk($$)p Fi(Z)34 b Fk(=)28 b(1$$)3328 1016 y Fc(\023)q(\033)1013 1416 y Fk(=)1376 1348 y(1)p 1181 1393 438 4 v 1181 1484 a Fe(P)1240 1499 y Fg(n)1289 1484 y Fk($$)p Fi(Z)35 b Fk(=)27 b(1$$)1629 1339 y Fh(p)p 1712 1339 59 4 v 77 x Fi(n)17 b Fh(f)p Fe(P)1896 1431 y Fg(n)1945 1416 y Fk($$)p Fi(Y)48 b Fh(\025)29 b Fi(y)2242 1431 y Ff(0)2281 1416 y Fi(;)17 b(Z)34 b Fk(=)27 b(1$$)22 b Fh(\000)h Fi(P)14 b Fk($$)p Fi(Y)48 b Fh(\025)28 b Fi(y)3111 1431 y Ff(0)3150 1416 y Fi(;)17 b(Z)35 b Fk(=)27 b(1$$)1376 1687 y Fh(\000)1481 1619 y Fi(P)14 b Fk($$)p Fi(Y)48 b Fh(\025)28 b Fi(y)1854 1634 y Ff(0)1893 1619 y Fi(;)17 b(Z)34 b Fk(=)28 b(1$$)p 1481 1664 749 4 v 1651 1755 a Fi(P)14 b Fk($$)p Fi(Z)34 b Fk(=)28 b(1$$)2255 1687 y($$)p Fe(P)2352 1702 y Fg(n)2401 1687 y Fk(\()p Fi(Z)34 b Fk(=)28 b(1$$)22 b Fh(\000)g Fi(P)14 b Fk($$)p Fi(Z)34 b Fk(=)28 b(1$$\))3297 1546 y Fc(\033)1013 1946 y Fk(=)1360 1879 y(1)p 1181 1923 407 4 v 1181 2014 a Fi(P)14 b Fk($$)p Fi(Z)34 b Fk(=)28 b(1$$)1598 1869 y Fh(p)p 1681 1869 59 4 v 77 x Fi(n)16 b Fh(f)p Fe(P)1864 1961 y Fg(n)1913 1946 y Fk($$)p Fi(Y)49 b Fh(\025)28 b Fi(y)2210 1961 y Ff(0)2249 1946 y Fi(;)17 b(Z)34 b Fk(=)28 b(1$$)22 b Fh(\000)g Fi(P)14 b Fk($$)p Fi(Y)49 b Fh(\025)28 b Fi(y)3080 1961 y Ff(0)3119 1946 y Fi(;)17 b(Z)34 b Fk(=)28 b(1$$)1376 2217 y Fh(\000)1481 2150 y Fi(P)14 b Fk($$)p Fi(Y)48 b Fh(\025)28 b Fi(y)1854 2165 y Ff(0)1893 2150 y Fi(;)17 b(Z)34 b Fk(=)28 b(1$$)p 1481 2194 749 4 v 1651 2285 a Fi(P)14 b Fk($$)p Fi(Z)34 b Fk(=)28 b(1$$)2255 2217 y($$)p Fe(P)2352 2232 y Fg(n)2401 2217 y Fk(\()p Fi(Z)34 b Fk(=)28 b(1$$)22 b Fh(\000)g Fi(P)14 b Fk($$)p Fi(Z)34 b Fk(=)28 b(1$$\))3297 2076 y Fc(\033)3393 2217 y Fk(+)23 b Fi(o)3539 2232 y Fg(p)3578 2217 y Fk($$1$$)1013 2508 y(=)1228 2440 y(1)p 1181 2485 142 4 v 1181 2505 a Fh(p)p 1264 2505 59 4 v 72 x Fi(n)1400 2383 y Fg(n)1349 2413 y Fc(X)1364 2623 y Fg(i)p Ff(=1)1510 2367 y Fc(\032)1684 2440 y Fk(1)p 1594 2485 228 4 v 1594 2576 a Fi(E)6 b Fk($$)p Fi(Z)h Fk($$)1849 2508 y($$1)p Fh(f)p Fi(Y)2043 2523 y Fg(i)2098 2508 y Fh(\025)28 b Fi(y)2251 2523 y Ff(0)2290 2508 y Fi(;)17 b(Z)2401 2523 y Fg(i)2456 2508 y Fk(=)28 b(1)p Fh(g)22 b(\000)g Fi(\027)6 b Fk(\()p Fi(P)14 b Fk($$1)p Fh(f)p Fi(Z)3153 2523 y Fg(i)3208 2508 y Fk(=)28 b(1)p Fh(g)p Fk(\))3448 2367 y Fc(\033)3545 2508 y Fk(+)22 b Fi(o)3690 2523 y Fg(p)3730 2508 y Fk($$1$$)1013 2829 y(=)1228 2762 y(1)p 1181 2807 142 4 v 1181 2826 a Fh(p)p 1264 2826 59 4 v 72 x Fi(n)1400 2705 y Fg(n)1349 2735 y Fc(X)1364 2945 y Fg(i)p Ff(=1)1510 2829 y Fi( )t Fk($$)p Fi(Y)1672 2844 y Fg(i)1699 2829 y Fi(;)17 b(Z)1810 2844 y Fg(i)1838 2829 y Fk($$)22 b(+)g Fi(o)2043 2844 y Fg(p)2083 2829 y Fk($$1$$)304 3132 y(where)963 3272 y Fi( )t Fk($$)p Fi(y)t(;)17 b(z)t Fk($$)27 b(=)1481 3204 y(1)p 1391 3249 228 4 v 1391 3340 a Fi(E)6 b Fk($$)p Fi(Z)h Fk($$)1646 3272 y($$1)p Fh(f)p Fi(y)30 b Fh(\025)e Fi(y)2014 3287 y Ff(0)2053 3272 y Fi(;)17 b(z)32 b Fk(=)c(1)p Fh(g)22 b(\000)g Fi(\027)6 b Fk(\()p Fi(P)14 b Fk($$1)p Fh(f)p Fi(z)32 b Fk(=)27 b(1)p Fh(g)p Fk(\))33 b Fi(:)304 3502 y Fk($$d$$)f(The)i(e\016cien)m(t)f(in\015uence)h(function)e(for)g Fi(\027)6 b Fk($$)p Fi(P)2120 3517 y Fg(\022)2159 3502 y Fk($$)28 b(=)f Fi(q)t Fk($$)p Fi(\022)s Fk($$)33 b(is)1435 3696 y(~)1444 3722 y Fl(l)1476 3737 y Fg(\027)1519 3722 y Fk($$)p Fi(y)t(;)17 b(z)t Fk($$)27 b(=)45 b(_)-45 b Fi(q)t Fk($$)p Fi(\022)s Fk($$)2041 3681 y Fg(T)2096 3722 y Fi(I)8 b Fk($$)p Fi(\022)s Fk($$)2271 3681 y Fd(\000)p Ff(1)2367 3696 y Fk(_)2365 3722 y Fl(l)2397 3737 y Fg(\022)2436 3722 y Fk($$)p Fi(y)t(;)17 b(z)t Fk($$)g Fi(;)304 3942 y Fk(and)33 b(the)g(information)c(b)s(ound)k(for)f Fi(q)t Fk($$)p Fi(\022)s Fk($$)g(is)g(giv)m(en)h(b)m(y)1735 4162 y(_)-45 b Fi(q)t Fk($$)p Fi(\022)s Fk($$)1888 4121 y Fg(T)1943 4162 y Fi(I)8 b Fk($$)p Fi(\022)s Fk($$)2118 4121 y Fd(\000)p Ff(1)2230 4162 y Fk(_)-45 b Fi(q)t Fk($$)p Fi(\022)s Fk($$)17 b Fi(:)304 4382 y Fk($$d$$)65 b(Geometrically)-8 b(,)1144 4356 y(~)1145 4382 y Fi(l)1174 4397 y Fg(\027)1244 4382 y Fh(2)1372 4357 y Fk(_)1339 4382 y Fh(P)41 b Fk(is)32 b(the)h(pro)5 b(jection)32 b(of)g Fi( )37 b Fk(on)m(to)2642 4357 y(_)2608 4382 y Fh(P)9 b Fk(:)2755 4356 y(~)2756 4382 y Fi(l)2785 4397 y Fg(\027)2856 4382 y Fk(=)28 b(\005$$)p Fi( )t Fh(j)3199 4357 y Fk(_)3166 4382 y Fh(P)8 b Fk($$.)304 4502 y(Th)m(us)34 b Fi( )26 b Fh(\000)739 4476 y Fk(~)740 4502 y Fi(l)769 4517 y Fg(\027)840 4502 y Fh(?)978 4477 y Fk(_)945 4502 y Fh(P)8 b Fk(.)1901 5896 y(10)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF