HW5_Sol - 3 ÑÐ ‡aÏ Ò cV ¨Îˆu q“ Ï ƒ...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3 ÑÐ ‡aÏ Ò cV ¨Îˆu q“ Ï ƒ c§£–3YV Ï Î y Ò y Ë “ Ô ÎÓ Ñ ‡ÐaÏ y { Ò “ hÌ rsq Ò y Ë “  hÌ Ë E  T 6hs 9ah†7IY(7Ie‡Q–T [email protected] q ¨ƒ~g [email protected]@aUu˜UQ([email protected] “• I A ‚ ’ gR f GI ` Î € 6 xA x wC f TTIRR sT e 6 [email protected]@§ƒ`h’BB`6BB`6}UDA { ‹ Dr [email protected] Í}±QQºW± ¹ z“ hÌkUQhe–Sˆd‡—c y hhYÄË »˜©Yghsufku([email protected] B97Y§‡8 @iue q sC IC Í 8A ºº Í  ICI • · ÌV E I € wR wg T s 9 Ig g 6 e I € 9 xwC Ê 9A 8 6 6 ’ ’ 7I @[email protected] vg huÉ b `` ‚T aA 3½ “ ˜ˆ—V † ft ©B6B€° ¯9 u cu Ts hPe · 3 w g T I  C I ‚ 8 w R  È · 3 8 I e g q ` ½ adYvQaQaPa(˜˜Da™QhYƒd ½ wg TI CI ‚ 8 w È IR 8I sr IT A 6 d 6T 9 A 8A 9 A IC € w … 9 sTIC A  6T s d 9 A YvQaUQa‡a(R  }(@Qut7Uv§B…Ä‚T ‚‡€ [email protected]#uUªCpg @UQ˜”h8 Shƒ7€ B9a@ 68 – ` ½ Y©aUQa‡a(dUT a©Uh˜p 6g wg I CI ‚ 8 wR w 9 A gT s € d ½ ‡†7j§hae}Qi‚w ˜§DFQehhk 6T Á u À vg „B€B6¢hYž8 §7(@ 68 ’ ‚T a¨d ½ Y©QaQaPa(£UT [email protected]@—eY‡a ‚C €x ’I’ 8 sw x CI • 9 ’ 8A CI f f s d 6 9 I eg 6 d IR ` ` A wg TI CI ‚ 8 wR w 9 A I 6T ’ 8A ¥g e 6 I eg wT d œ › † TA 3 hYU‡Â%–D†Â› ¹ Á Æ xÀ aw v(aSšC„he q ‚T aÇ­%%DA ½ [email protected]@—eYªg7I [email protected] – ÁÀ 8 6 g R A … I ` ` A œ › † T w g T I w  I 6 T ’ 8 A ¥ … 9 I e g d c ’ V g C A f € w u ft 3 Äft }vt ft ±u Åu u 3 Äft ¹ —ÆÁ @Š † ‘ Á @Š À À ±u gA eg 8I 6  ICA I D§YdQa‚ u}UD£‰ pà Äom `c V gCA f … w 9 sTIC I eg … w IT sAR I x wg I CI ‚ 8 wR w 9 A 6 [email protected]@u%g @UQ©hYuu©UhDQ7e‡d ½ Y“aQaPa(dT aHB9B9“• d œ › † TA {u ·Á À T s ` I 9 A ‚ I € AT I eg wg I CI ‚ 8 wR w Â%iDed Yft ([email protected] r h‡e q 7hs ahfka‚fhY“Y}aQaPa(¢Yg { ‹ y ˆ·PŒŠ r UhDQ¢UT a®B9B9“¾”Y%QaUQa‡a(R ¿  IT sAR w 9A 6 • œ wg TICI‚ 8w [email protected] { ‹ Dr (@Qhv7U”‡Dx‚T ‚‡€ [email protected] g @QU“™P£› y DYT eQI ‰y @Š r ukg „B€B6”hYF(@ 68 ’ 6 e y IR 8I sr IT € 8A d 6T 9 A 8A 9 A IC 6 9 sTIC A € x d œ TA Tg 6 G { ·  … w 6 9 I eg IR ` ` ½ ‹ » “ ·c  ± ººº ¹ ¸ ° “ ·  ° ‚T aA “ ¼‡P¸ £E ™y Yu‡¸ !QQ²± ®YV ©B6B€¯ 9  yy ŒŠ ©B6B€¯ 9  d ´ @h’ [email protected] ¶ ¶ I eg € pµ %om `gCA f 6 eg C … ’ I 6 sr IC 6  6 6C • [email protected] @Y˜aªw¢7UC @v7U˜T u8 vg ‚–„w ´ p³ ®om ` ± c u ° 9 ` 6 d œ › † TA c u C … ’ 8 s w x I 6 8 ™ w 8 6 ICI eg d 8IT w R I x 9 s wR ¡ Ÿ € 8 ²œ “ ˜ˆ—V ftz©¯u €BB6®Bd7I u­¬«D‰˜ˆ—V ft [email protected] @u©h‰T [email protected][email protected](‘s¨‡DA IT sA I § ` ¤ † 8 e • [email protected] w QIh–¦Ÿ w ˜ˆ—V ft Uuuh8 ‚D7U(7juahW€ 7hhfT ˜˜ˆ—V vt žŒŠ “ Qh˜£Ÿ “ ˜ˆ—V ft c u wT d  6TA ICR I ’¥ 8 w 8 9 IC s f 6 c u ` ¤ † 8I e • cu 8I ` ¡ Ÿ g 9 d 6 eg I‚ C f ` › † TA c u C … ’ 8 sw x I 6 8 ™ w 8 6 ICI eg d — € 8A C Que q –¢ QI –‚T @Y¢a‚wUhžw q œ ƒ„D˜ˆ—V ft ašw@haeYg @h˜h†T sUQhY¨˜™PD˜aw – p• %om ` { zWŒŠ s”}‰zxvayq uw ’ † ‘  r q “ { y w u tr d `† ‘   6 €AT A I €A I eg 6 e d† w 9A sr I w 8A eg TT 9 ICA 6 e • ‹ Š TI 6g9A 6CC ICA ICI eg T QzƒŒŠh8 eU‚‰TDka‚T–uY‰T [email protected][email protected]D§Y‰UQI [email protected]Œ}QkB€vjah‚ ‚UDA y UDFUQuY‰DA gPQaQ}}aA‚}hY%T pT @e q ˆ`‡~(aYy8 6FT aƒ‚ ‚DUCakpaw y UDUQhY%D§YW~g [email protected]@aUh}uY– 6T |zxv7sq 8I‚I I € T I eg 6 6 †… „V 9 A 6CCA I w € C ICA ICI eg gA eg € 6 xA x wC f I eg { y w u t r pn §om l`…u‡UhfkeYg “•–a–jSai”8 QhYg 7h§QaDvfedDQ™QYU˜—ea7I w wC A 6 Cw T’Cw • 6 CI e 6 I d 8IgAg I x 8AR fIgT RA € • ’ 8AgT I’ 8 s g 6 ’ I sr IC gA ‰ … w w f I e … [email protected]@h”wY“T £7UC [email protected] [email protected] B69vuayDƒQa‚ u£€ [email protected] vUQutWT §e q g sw 8A TI 6  9A 6TA x 8 6gTI sr 6 i CIg fA e 4 dc3 `XV I 6RCI G E C 9 6 [email protected] [email protected] 7 45 3 2 1 0 ) '&  $ "       © ¥ ¦ ¤ ¡ %§(!%(¨%#!¨¨¨§¥ ¢£¢ b Ð Ð ¹ aÏ ¹ jÏ ë “ ‡¸ » fG» ø ¢ ¢£Ô ÿÿÿ ý ¡ë HÔ ø  “ ÿÿÿ ý ¡ë HÔ ø  “ þ‡a‡§÷ö %PQI žE ÿÿÿ ÿÿÿ wT dc w C …V CI x s 8 9 A IC A 9 6 AgCIR UƒYa3 yy [email protected] @8 avUQ( 6T ƒûý  7DQ“ha¢([email protected] d ITAR C s w 8ü ` ÷ CI x € s 8 9 A IC € 8A C » f G E gA eg 8I 6 ICI • ‰ Í … w IR 8I ’ 8I fI ’ 6 I eg wg I s ’ 6 9 A sr I 9 A 8 ™ I úú ø 7û ÄÔ ù“ B‡‡ Ï Í ÷ö ¬‡QI »˜[email protected] uUQ«†I£}` { Ï Dr up(@[email protected] ”hY¢Y“ujT ˆ€g [email protected][email protected] q Ð Ð Ð ò y f G ¹ jÏ “ ò y f G ¹ aÏ E “ ò y ¹ aÏ f G ¸ VfG» Ï Í ÷ö ‡QI E Ï Í ÷ö PQI Ï Í ÷ö ‡QI E “ ˆ‡c  [email protected] ˜E    õ  ¸ … w 8 6 R 8 … 6g CIgR CA R eg I 9 s 9 A Ög 9 gT ` • 9 6 I CI ‚ 8 wR gR h‡¨u”aw vg(@hªsFBRvUT 6‚QY([email protected]@(BRaQRT vQI ŒdvUU 6C – “UBA™8 aQaPa(“(aˆA… 8 pQIPjpg 6§B…„h8 [email protected](Rp‡a 6„(@QIhv7UT%T @YpI [email protected]@[email protected]}h8 ‚QYQj’ 6 T w ’ 6 I €CIgI 8I eg ’ 8A d w I CI ‚ 8 w g e € IR 8 sr I 6 eg x 6C ‚ € w ’ 8AC gA e • I 6 €CIgI w ’ I 8 eg x I ô • 9 I CI ‚ 8 wR ó  IR 8I s IT I e TI w ò · Yg7QIudYawe£‰£“UBA8 6aUQaPa(“¹Äƒ { ‡¸ r (@Qutr7UFhYg}Q‡iè“` Hy Yc Ís‡QQ‘± ¹ VÍ “ ‡†QI ¶ ¸ g ±ººº € 9 xwC Ê 9A 8 6 6 ’ ’ 7I @[email protected] vg huÉ i cV ° §ˆÎ® q pB6B€¯ 9  “ ¨ˆÎÄË cV d I ’ 9R 8 wR 8A [email protected] Q§a(DQR I • ’ 8A d I 9 A ‚ ’ IgR I f GI I eg … w 6C gI  8AR I • c 9 x 6CA ‚ € w ’ 8AC A g w V g 8AgT 8 wR A 6 c V Ë IR 6T d ’ 8 [email protected] ahF7Y(7®‡QfhYƒupB’‚¬QaƒDQ†«Œ7I [email protected]}ahˆ8©‡DvUha(F}T «§ˆÎĆ(@8 [email protected] cV ° §ˆÎ® q ©B6B€¯ 9  “ ˆ‡§ˆÎÄË žE cV» ` Î d I 9 A ‚ ’ IgR I f GI T 6 wg ` ` A TI CI ‚ 8 w ¨ƒ7hs ah†7Y(7e‡Q–Yg dYxST aQaUQa‡a(R g [email protected][email protected] @[email protected]`B6B`¬uD7k˜I @}a‚† 6T y uu˜(@8 ‚Äd ´ Œh’ uYïuUªC‰§Qhe q 6 gA eg •w 8 g I • dT 9 x 6CA ‚ € w ’ 8AC ` 6 … w 8A I € 9 f € AT A ·  Ì IR 6T ¶ ¶ I eg € w … d 8I ° ° c §ˆÎV  q ©B6B€¯ 9  “ hy Ì ©B6B€¯ 9  Ë E  `c 6T 9 A 8A 9 A IC € w … d 6 A AV 6 9 I eg ’ 8A 8 6gR 8 … I eg … w CI ’C w I eg I  8A R G Y‚T ‚‡€ [email protected]@@8 auDY“g [email protected] v(§hšs[email protected] wg 9 6TT w f 6 6 6 e • 6 I 8 w 6 8 6gR 8 … T s w s 6g 8 wR A d 8 6 6 8 ™I ’ € x ’ 8A dT s w s 6g 8 wR 6 8 6gR 8 YI @x ‚a®T ¢g [email protected]8 £haT îaw v(§hšs”hauP8 v‡a(d%§aw vg @hQj²‡”§D–‚hah‡8 v‡a(¢T îaw v(@hªs… I eg gA eg 8I 6  ICA I • IT sAR I x 9 6TT w f 6 6 ` Ë 8 6gR 8 … I eg … w I 6T 6 6 9 I eg I gAg I • dg G [email protected] uWUD˜«UuDQ7®I @x ‚UaepT T @e q Äîaw v(@[email protected]aB’‚h8 ƒg [email protected] ´ ° cV ° §ˆÎ q ©B6B€¯ 9  “ hy Ì Ë ©B6B€¯ 9  E  d 9 A ‚CIg 6 I eg 8 w 8 6gR 8 … gA eg … w € s 6 6 uw ’ B`ahUQY‡8 WhY”aaw v(@[email protected]@[email protected] „€ ’ 8A € s 6 GA € I 6 8 A ’ 8 ™ 8AR I • d 6 gA ` ’ I ’ 8 s w x 9 IT 6 6 9 A ‚CIg 6 ’ I ’ 8 s w x ’ IT 9R A 8 w 8 6gR 8 @Dí§–€BÄD„FYg §h™–@hDQF«!ST [email protected] q h7j§haeƒB…7UYg }T ®ahUQY‡8 [email protected] Q“žaƒaw v(@hªs… T sw s 6g 8w € 8A d 6T 9A 8A 9A IC … w 9 sTIC A  6T ì ` ’ I’ 8 sw x hah‡8 vPa(RPD§‚T ‚‡€ [email protected] @QU}žh8 [email protected] 6T 7ë ê I @[email protected]‚hUT Ë 9 x 6CA ‚ € w’ 8AC I eg gA eg •w e w ’II8 I •d 9A 6 8 YgF7Qh}iu7€ [email protected] q 7UCaQhe q ([email protected] „uihY–Dy˜vh‡†UT a“T [email protected]@8 75 §ufb ` € I wI IR 8I CI ‚ 8 w 4 ’ IgA 6 € w è I eg TA 8 •w 8 g w 9 A 6 6 e • dC 9 6 4 … w CIg A e 4 6 X ` € IC w  6 s 6 eg w ’ I ‰ `c 3V 6 I 9 A ‚ ’ IgR I f GI I eg I 6T 6 6 9 I eg I ‚w € I • dgT [email protected] ©aBia3ç7UaQIhe q u8 ‚ThxT @Yfjp£§YaY8 ©hs ahf7Y(7®‡Q¬hY¬jB’‚h8 –g „B€B6puY%avk©«jvUU 6C – æ³nåâ ä än n ãâ ß Sh[email protected]Ã à §SPà áàÞ ˆ‡c¨ˆÎÄË ˜E “ ˆ‡c y hYÄË ˜E pB6B€¯ 9  V» ·  ÌV » ° d IR 8I Ý ` 8 6gR 8 … ’ I ’ 8 s w x A w 9 A 6 Ë d Ë … w 6 s 6g 8 wR € 7(@[email protected] v(@[email protected]}dUT a“T £Äħu”ˆ€g §P8 v‡a(ž‡x ˆdDB3a„ ¬9ahUQY‡8 d7Taw QƒhYgda7Ih8hQj†T 6£Ëƒ(§ 68 ’ [email protected] [email protected] §e q §Ú›hŒd ´ Œh’ ‡h‚T (‹ Í ‡ d » A ‚CIg 6 ’ I 9R I e 8w ’ ™I’ I R ` Î Û ›  Ì g A e g T 9 f 6 6 ` Î Ù ‚×  Ì ¶ ¶ € x d Ö Ø T 9 x 6C ‚ € w’ 8AC 6 … w sT QI @[email protected][email protected] 6T  Ì}(@ 68 ’ [email protected] [email protected] [email protected] UDv§hs Õ IR `c wg9 A sr I 6 I 6T ’ 8A ¥ … 9 I eg gA eg •w eT wg 6 gTAg C ° c3 aYV cV §Îˆ q °©6B€B¯ 9  “  y Ì Ë E ©B6B€¯ 9  d 8 6gA sr I I eg … w TI 6T egw x … w 6 9 I eg IgAg I • d • §aw [email protected]}uYuu˜QjB’‚”Yaeuu–g „B€B6WhY“aDv©«ƒ“vw ´ i `g 8ICI 6 ’ 9g e 9 vPQUQ®& hy€ v‡a B6‚T [email protected]%T ŒB…7Yg paw @”—ea7‡7Uha(H… Õ [email protected](DBAvD˜%7heavYDhYkQI ’ x A TC w € € w ’ 8AC 6 9 IT 6 g 9 f R A I d ITC s wR `TIC s  ™ ’ 8A I ’ wR x 9gA $ ’ I R AggA I eg I ` € IC wI 6 9 ACg 8I 4 I eg 6CI ‚ Ö 8TI w ’ gA eg  6 w è ` IR 8 6 CA ‚ 9 f € A 7UaQhe q g B€6 ¶ a‚Y‡Q¨hYª€B…‚Qa%g @UQ‡j“D§Yh8 ui–7(@DBASDƒ©I §ka‚T I g … g w C I A r I eg e 6 •  C w d 8A I € 9 f € AT e 6 • » E IR 9 fIC wg !  g 8AgC w f 6 6 6 gA eg Ig [email protected] [email protected] @ka‚”Yg FH‡ Í žƒ([email protected]Y" ‡DvUaekB€“T Fg [email protected] ´ Ñ ba3 V CA …b· »  cb· Ó 3 “ ò ¹ Î ò aaa3 ˆÎV ¹ “ ò ¹ á‡c Í §D˜ » “  aaa3 “ ‡ Í ˜E gA eg •w 8 g I [email protected]‚hP“£‰ € 9 xwC Ê 9A 8 6 6 ’ ’ 7I @[email protected] vg huÉ  `•9 “UBA™ 68 ¸ ›  ¸ T s ` 3 g 8AgT 8 wR A 6 8 6gR 8 … 6g 6CIgR ACA R T 6 ’ 8A d wCI¨ T €A 9 A 6 Ö 9 x 6CA ‚ € w ’ 8A ¦ 6 ­WPkh‡e q ak‡DvUha(F©T žaw v(§hšs}BRvT ‚QY([email protected] [email protected]}• akT e7I @[email protected] §T @e q I 6 •CI egw UT FUQhYa£„ ©Ä¥“ ¸ yq „ ¢¤ B…6 3 “ { ¤ r “ õI8w 7ha– 6T I I Ý 3 g Ag 8 w A 6 • 8 6gR 8 … 6g 6CIgR ACA R A TA e gA eg ¸ 9 x 6CA ‚ € w ’ 8AC A ’ 8 ™ wg ’ II 8 I UCQ|%`ap‡8DvUTha(R©T [email protected] v(§hšspBRvUT ‚QY([email protected]}D§«D§Yî„I @DBA‚Dh[email protected] d“YBA9s8 „I(@QIaUQIa‡a(R©aw – a3}P8DvUua(“©T £aw v(@hªs}BRvUT ‚QY([email protected] [email protected] [email protected] ‰ • 6 R 8 C ‚ 8 w C ` g AgT 8 wR A 6 8 6gR 8 … 6g 6CIgR ACA R I eg … w 6 9 I eg gA eg 6 IIT I • gA 3 “ Ñ “ ¢ ë £Ô ø ©B6B€¯ 9  “ [email protected] ˜E pB6B€¯ 9  c¸ VfG» ° ø¢° d 6 9 I eg  6 gAg d vg „B€B6uY„h8 ÄDvƒuw ’  tn FDm c ‡y ”ˆfWr 8s 8I‡ F8F88‘ q ” t §q – l x r c ‡w y 8s 8§j‡ ” ƒ ” t §q – l x r c™‰ …“ F8h88‰ w c††‰ …“ F88h88‰ w c s ˆr m p v u 8Fj§8FDo 8• tn FDm c e d 8` D8Fjr t 8hFDjgD˜ d @Fj§8F88‘ q ass k Y s ˆ W fr ‘ Y s kr ˆ f W r s t gD8FD8Iy ` hk p 8• r pqo nml Y – c8s8sFˆjr§q8p88g F88d §D8DIF8hgD˜ d hFDf i i f e r a s X W V w ˆ W —r ‘ Y ˆW c 8s e d 8` FD” ` ”  §888† e 8hhF8—  ”ˆ r …™ ™˜ Y ˆW ‚ 888h88h8` §8ˆ p 8• ` `  u Y – c8s ` ”  ” t ” ‡8FD88I‡ §88hY “’ ‘‰ˆ r †…„ wu c 8‚ x y 8D€ y x DvY ` ƒ t fe cb 8s D` a ` §888hY 88d r qpig c b a ` Q8DV Y XW UT S R P HG E CB A 9 7 7 [email protected]@887 65 4 3 210 (10) ( ( ' Empirical vs. Theoretical CDF for N = 10 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −5 0 5 Empirical vs. Theoretical CDF for N = 100 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −5 0 5 Empirical vs. Theoretical CDF for N = 1000 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −5 0 5 X ...
View Full Document

This note was uploaded on 01/19/2012 for the course ECEN 646 taught by Professor Serapsavari during the Fall '11 term at Texas A&M.

Ask a homework question - tutors are online