ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÁÒÜ ½ ÁÒØÖÓÙØÓÒ ¾ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ
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- Bridget Carpenter
- 6 years ago
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1 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÙÑÔ ÐØÖ ÓÖ ÙÒÖØÒ ÝÒÑ Ý ØÑ ÛØ ÖÓÔÓÙØ º ÓÐÞ ½ º º ÉÙÚÓ ¾ Áº ÈÖÖÓ ½ ʺ ËÒ ½ ½ ÔÖØÑÒØ Ó ÁÒÙ ØÖÐ ËÝ ØÑ ÒÒÖÒ Ò Ò ÍÒÚÖ ØØ ÂÙÑ Á ØÐÐ ËÔÒ ¾ ËÓÓÐ Ó ÐØÖÐ ÒÒÖÒ Ò ÓÑÔÙØÖ ËÒ Ì ÍÒÚÖ ØÝ Ó ÆÛ ØÐ ÆËÏ Ù ØÖÐ Ö Á ÓÒÖÒ ÓÒ ÓÒ Ò ÓÒØÖÓÐ ÑÖ ½ ¾¼½ ÄÓ ÒÐ ÍË
2 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÁÒÜ ½ ÁÒØÖÓÙØÓÒ ¾ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ
3 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÁÒÜ ½ ÁÒØÖÓÙØÓÒ ¾ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ½» ½
4 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÁÒØÖÓÙØÓÒ ÈÖÓÔÓ ÒÖÓ ÊÑÓØ ØØ ØÑØÓÒº ÄÌÁ ÌË ÛØ ÓÙÒ ÌÎ ÙÒÖØÒØݺ ÆË ÛØ ÖÓÔÓÙØ º ÍÒÖØÒ ÈÐÒØ ËÒØ ÑÙ ÙÖÑÒØ ÆØÛÓÖ ÛØ ÖÓÔÓÙØ ÊÚ ÑÙ ÙÖÑÒØ ËØØ ØÑØÓÒ ØÑØÓÖ ½» ½
5 ËÓÒ Ã Ò ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÈËÖ ÖÔÐÑÒØ ÈÖÚÓÙ ÛÓÖ ÓÒ ÐØÖØÙÖ ÃÐÑÒ Ú ÂÙÑÔ ÃÐÑÒ ÐØÖ Ò Ò ÖйØѺ ÇÒ¹ÐÒ ÓÑÔÙØØÓÒÐ Ó Øº ÂÙÑÔ ÐØÖ ÈÖ¹Ò Ò º ËØÓÖ Ò ÐØÓÒº ¼º¾ ¼º¾ ½½½½ ½½½¼ ½½¼½ ½½ ¼¼ ½¼½½ ½¼½¼ ½¼¼½ ½¼¼¼ ¼º½ ¼º ¼º ½ Ö Ø Ã Ò ¾» ½
6 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÈÖÚÓÙ ÛÓÖ ÓÒ ÐØÖØÙÖ ÍÒÖØÒ ØÑØÓÒ ÄØÖØÙÖ ÐØÖ ÓÒ ØÒØ Ú ÙÐÐ ÙÑÔÒ ÑÓº ËØÐØÝ ØÖÓÙ ÄÝÔÙÒÓÚ ÕÙØÓÒº ÇÙÖ ÔÔÖÓ ÌѹÚÖÝÒ ÙÒÖØÒØÝ ÓÒ ØØ ÑØÖܺ ÅÖÓÚÒ ÒØÛÓÖ ÑÓÐ ÑÙÐع Ò ÓÖ ÖÓÔÓÙØ µº ÓÚÖÒ¹ ÙÑÔ ÐØÖº ÌÖ¹Ó ØÛÒ ÓÑÔÐÜØÝ Ò ÔÖÓÖÑÒº ËØÐØÝ ØÖÓÙ ÓÙÒÒ Ó ÓÚÖÒ ÖÙÖ ÓÒº» ½
7 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÁÒÜ ½ ÁÒØÖÓÙØÓÒ ¾ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ» ½
8 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÁÑ λµ ËÝ ØÑ ÖÔØÓÒ ÈÐÒØ ÈÐÒØ Û, Ú Ü +½ = (+ ) Ü + Û, Ý = Ü + Ú, ÒÔÒÒØ Ù Ò ÒÐ {Û Û Ì } = Ï, {Ú Ú Ì } = Î. ÍÒÖØÒØÝ ½ λ ÒÚÐÙ Ó + = À, Ì Á. ¼ ¹½ ¼º Ê λµ ½» ½
9 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ËÝ ØÑ ÖÔØÓÒ ÆØÛÓÖ ØÖÒ Ñ ÓÒ ËÒ ÓÖ ½ Ý ½, θ ½,+½ = ½ ÐØÖ Ñ ËÒ ÓÖ ¾ θ ¾,+½ = ½ Ý ¾, ¾ ½ + ½ θ ¼ ½ θ +½ ½ ½ ÚÐÐ Ñ ÙÖÑÒØ Ñ = θ Ý = θ ( Ü + Ú ).» ½
10 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ËÝ ØÑ ÖÔØÓÒ ÆØÛÓÖ ØÖÒ Ñ ÓÒ ËÒ ÓÖ ½ Ý ½, θ ½,+½ = ½ ÐØÖ Ñ ËÒ ÓÖ ¾ θ ¾,+½ = ½ Ý ¾, ¾ ½ + ½ θ ¼ ½ θ +½ ½ ½ ÅÖÓÚ Ò ØØ θ Θ = {ϑ ¼,ϑ ½,...,ϑ Ö }, Ö = ¾ ÒÝ ½, ÃÒÓÛÒ ØÖÒ ØÓÒ ÔÖÓÐØÝ ÑØÖÜ Λ = [Ô,] Ô, = ÈÖ{θ +½ = ϑ θ = ϑ }. ÌÓØÐ ÔÖÓÐØ π = ÈÖ{θ = ϑ }º» ½
11 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÈÖÓÔÓ ÐØÖ ØÑØÓÒ ÐÓÖØÑ ˆÜ = ˆÜ ½, ˆÜ = ˆ Ü + Ä (Ñ θ ˆÜ ). ÂÙÑÔÒ Ò ÖÐØ Ä ØÓ θ Ä(θ ) = Ä θ = ϑ ÛØ Ä(θ ) L = {Ä ¼,..., Ä Ö } Ò Ö = ¾ ÒÝ ½º ÅÒ Ò ÓÐ Ò L ØÓ Ú ÚÓÖÐ ØÖ¹Ó ØÛÒ ÓÑÔÐÜØÝ ØÓÖµ Ò ÔÖÓÖÑÒ ÓÖ ÐÐ Ñ Ð ÙÒÖØÒØ º» ½
12 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÁÒÜ ½ ÁÒØÖÓÙØÓÒ ¾ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ» ½
13 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ØÑØÓÒ ÖÖÓÖ ËØØ ØÑØÓÒ ÖÖÓÖ Ü = Ü ˆÜ µ Ü = (Á Ä θ )( Ü ½ + ½Ü ½ + Û ½) Ä θ Ú. ÖØ Ý ØÑ ÛØ Þ = [ Ü Ì Ü Ì ] Ì Þ = ( + À ½ )Þ ½ + Û + Ú ÛÖ [ ] [ ¼ =, À = ¼ (Á Ä θ ) À (Á Ä θ )À ], = [ ] [ ¼, = (Á Ä θ ) ] [, = ¼ Ä θ ].» ½
14 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ØÑØÓÒ ÔÖÓÖÑÒ ÜÔØ ÓÚÖÒ ÑØÖÜ Ö {Þ Þ Ì } = {Þ Þ Ì θ = ϑ }ÈÖ{θ = ϑ } = =¼ Ö È,π, =¼ ÅÓÐ ÓÚÖÒ ÑØÖ Ö π È, = Ô, ( + À ½ )È ½,( + À ½ ) Ì π =¼ + Ö =¼ π Ô, ( Ï π Ì + Î Ì ). ÊÙÖ ÓÒ ÓÒ Ø ÑÓÐ ÓÚÖÒ P = E{P ½, ½} ÛÖ P (È Ø,¼,...,È Ø,Ö) Ò E{ } (E ¼ { },...,E Ö { })º» ½
15 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ Ò Ò ÓÐ Á Ò L ØÓ ÑÒÑÞ Ø ÓÙÒ Ó Ø ÜÔØ ÓÚÖÒ ÑØÖÜ ÓÖ ÐÐ Ñ Ð ÙÒÖØÒØ Ò Ø ØÝ Øغ ÑÒÑÞ L, P ØÖ Ö =¼ È π ÙØ ØÓ E{ P, ½} P ¼, P ¼, Ì Á ÛØ P ( È ¼,..., È Ö ) Ò L = {Ä ¼,...,Ä Ö }º ½¼» ½
16 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÌÓØÐ ÜÔØ ÓÚÖÒ ØÖ ÓÙÒÒ Á (L, P) Ö Ø ÓÐÙØÓÒ Ó Ø ÓÔØÑÞØÓÒ ÔÖÓÐÑ ÓÖ ÒÝ P ¼ ¼, ÛÒ, P P ÓÖ ÐÐ Ì Á ËØ Ó Ø ÔÖÓÓ Á {G } ÛØ G ¼ P ÓÙÒ Ý P Á {Q } ÛØ Q ¼ P ÒÓÒÒÖ Ò ÙÒØÐ Ö P ÌÒ Ø ØÖØÓÒ P = E{P ½, ½} ÓÙÒ Ý Pº ½º ÌÖ Ó P ½ ¼º ¼ ½¼ ¾¼ ØÖØÓÒ ½½» ½
17 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÌÖØÐØÝ ÐÒ ÛØ ½ Ò E{ P, ½} P ¼ ÑÔÖØк Á ÓÙÒ ÐÑÒØ Ó E{ P, ½} E ( P, ½) È Ψ È ¼, ½ Ì ½ Á. Á α ¼ Ò É ¼ Ù ØØ α ½ Á Ì È ¼ ØÒ (+ )É(+ ) Ì (É ½ α Ì ) ½ Ì +α ½ ÀÀ Ì. Ψ = Ö =¼ + π Ô, ( ( È ½ Ì α ) Ì π Ö =¼ π ( Ô, Ï Ì + Î Ì π +α ½ ). ) Ì À À ½¾» ½
18 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÆÙÑÖÐ Ù ÅÁµ ÑÒÑÞ L,P,R ÙØ ØÓ ØÖ Ö =¼ È π È Õ Õ À Õ Ï Õ Î Å ¼ ¼ ¼ ᾱ ¼ ¼ ¼, = ¼,..., Ö, Ï ¼ Î È Ê = Á. ÛØ Õ = = Î = [ Ô¼, π ¼/π Ô Ö, π Ö/π ], ᾱ = Ö, =¼ Ö Î, =¼ À = È = Ö À, =¼ Ö È, =¼ = Ê = Ö Ö, =¼ Ê =¼ Ö α Á, =¼ = Å = Ö, =¼ Ö Ì Ê α, =¼ Ï = Ö Ï, =¼ ½» ½
19 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ Ò ØÖ¹Ó Ò ÓÐ ÁÁ Ò L ØÓ ÖÙ Ø ÐØÖ ÓÑÔÐÜØݺ [ ] [ ] [ ] [ ] ݽ, Ø ½ ¼ ½ (θ ) =,,. Ý ¾, Ø ¼ ½ ½ }{{} Ľ ˽º ÓÒ ØÒØ Ò Ä ½ º ½» ½
20 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ Ò ØÖ¹Ó Ò ÓÐ ÁÁ Ò L ØÓ ÖÙ Ø ÐØÖ ÓÑÔÐÜØݺ [ ] [ ] [ ] [ ] ݽ, Ø ½ ¼ ½ (θ ) =,,. Ý ¾, Ø ¼ ½ ½ }{{}}{{} Ľ ľ ˽º ÓÒ ØÒØ Ò Ä ½ º ˾º ÆÙÑÖ Ó Ò ÓÖ Ä ½ Ä ¾ º ½» ½
21 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ Ò ØÖ¹Ó Ò ÓÐ ÁÁ Ò L ØÓ ÖÙ Ø ÐØÖ ÓÑÔÐÜØݺ [ ] [ ] [ ] [ ] ݽ, Ø ½ ¼ ½ (θ ) =,,. Ý ¾, Ø ¼ ½ ½ }{{}}{{}}{{} ˽º ÓÒ ØÒØ Ò Ä ½ º ˾º ÆÙÑÖ Ó Ò ÓÖ Ä ½ Ä ¾ º Ë º ËÑÔÐÒ ÒÖÓ Ä ½ Ä ¾ Ä º Ľ ľ Ä ÅÒ Ò ÓÐ Ò L ØÓ Ú ÚÓÖÐ ØÖ¹Ó ØÛÒ ÓÑÔÐÜØÝ ØÓÖµ Ò ÔÖÓÖÑÒ ÓÖ ÐÐ Ñ Ð ÙÒÖØÒØ º ½» ½
22 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÁÒÜ ½ ÁÒØÖÓÙØÓÒ ¾ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ½» ½
23 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ËÝ ØÑ ØÙÑ ÈÐÒØ ¼. ¼.¾ ¼. ¼.¾ ¼ ¼.¾ ½ ¼. ¼. = ¼. ¼. ¼., = ¼.½ ¼.½ ¼.¾, = ¼. ¼. ¼., ¼. ¼. ¼.¼½ ¼ ¼.¾ ¼.¾ ¼.¾ ¼.½ ¼.½ Ì ¼.½ ¼.½ ¼.½ ¼.¼ ¼.¼ ¼.¼½ ¼ ¼ À = ¼.¾, = ¼.½, Ï = ¼.¼ ¼. ¼.¼, Î = ¼ ¼.¼½ ¼, ¼.½ ¼.½ ¼.¼ ¼.¼ ¼.¾ ¼ ¼ ¼.¼½ = Ò(/). ÆØÛÓÖ ÔÖÓÐØÝ Ò ÓÖ Ù ¹ Ù Ô = [ ¼. ¼. ¼. ]. Ò ÓÖ Ð¹Ð Õ = [ ¼.¾ ¼. ¼. ]. ½» ½
24 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ØÙÐ ØÖ Ó Ø ØØ ØÑØÓÒ ÖÖÓÖ ÓÚÖÒ ÌÖ¹Ó ÆÙÑÖ Ó Ò Ë½ ½ ˾ Ë º ¾º ¾ ½º ½ ˽ ˾ Ë ÌÖ Ó P ˽ ¼º ¼ ¼¼ ½¼¼¼ ½¼¼ ¾¼¼¼ ¾¼¼ ¼¼¼ ¼¼ ÑÙÐØÓÒ ØÑ Ò ØÒØ Ø ½» ½
25 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÁÒÜ ½ ÁÒØÖÓÙØÓÒ ¾ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ½» ½
26 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÓÒÐÙ ÓÒ ÚÐÓÔÑÒØ ÍÒÖØÒ ÔÐÒغ ÅÙÐع Ò ÓÖ ÒØÛÓÖ ØÑØÓÒ ÛØ ÖÓÔÓÙØ º ÂÙÑÔ ÐÒÖ ÐØÖº ÌÖ¹Ó ØÛÒ ÔÖÓÖÑÒ Ò ÓÑÔÐÜØÝ ØÓÖµº ÙØÙÖ Ö Ö ÖØÖÞØÓÒ Ó Ø ÔÖÓÖÑÒ Ò ÓÑÔÐÜØÝ ØÖ¹Ó º ½» ½
27 ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÙÑÔ ÐØÖ ÓÖ ÙÒÖØÒ ÝÒÑ Ý ØÑ ÛØ ÖÓÔÓÙØ º ÓÐÞ ½ º º ÉÙÚÓ ¾ Áº ÈÖÖÓ ½ ʺ ËÒ ½ ½ ÔÖØÑÒØ Ó ÁÒÙ ØÖÐ ËÝ ØÑ ÒÒÖÒ Ò Ò ÍÒÚÖ ØØ ÂÙÑ Á ØÐÐ ËÔÒ ¾ ËÓÓÐ Ó ÐØÖÐ ÒÒÖÒ Ò ÓÑÔÙØÖ ËÒ Ì ÍÒÚÖ ØÝ Ó ÆÛ ØÐ ÆËÏ Ù ØÖÐ Ö Á ÓÒÖÒ ÓÒ ÓÒ Ò ÓÒØÖÓÐ ÑÖ ½ ¾¼½ ÄÓ ÒÐ ÍË
28 ÊÑÖ ÈÖÓÓ ÁÒÜ ÊÑÖ ÈÖÓÓ ½» ½
29 ÊÑÖ ÈÖÓÓ ÅÖÓÚÒ ÖÓÔÓÙØ Á Û ÙÑ ÑÙØÙÐÐÝ ÒÔÒÒØ ÅÖÓÚÒ ÔØ ÖÓÔÓÙØ ÓÖ Ò ÓÖ ØÖÒ Ñ ÓÒ Ù ØØ ÈÖ{θ, = ¼ θ, ½ = ¼} = Õ, ÈÖ{θ, = ½ θ, ½ = ¼} = ½ Õ, ÈÖ{θ, = ½ θ, ½ = ½} = Ô, ÈÖ{θ, = ¼ θ, ½ = ½} = ½ Ô, ÓÖ ÐÐ = ½ ØÓ = Ò Ý ØÒ ÐÑÒØ Ó Ø ØÖÒ ØÓÒ ÔÖÓÐØÝ ÑØÖÜ Λ = [Ô,] Ó θ ÓÖ, = ¼,..., Ö ÐÙÐØ Ô, = Ò Ý =½ ÈÖ{θ, = ϑ, θ, ½ = ϑ,} ÛÖ ϑ, Ø ¹Ø ÓÒÐ ÐÑÒØ Ó ϑ º ½» ½
30 ÊÑÖ ÈÖÓÓ ÈÖØÓÖ Ì ÔÖ ÒØ Ö ÙÐØ Ð Ó ÔÔÐÝ Ò Ø Ó Ø ÔÖÓÔÓ ØÑØÓÖ Û ÔØ Ø ÔÖØÓÖ ˆÜ = (θ )ˆÜ ½ + Ä(θ )(Ñ ½ θ ˆÜ ½). ÁÒ Ø Þ = ( + À ½ )Þ ½ + Û + Ú ÛØ [ ¼ = (θ ) (θ ) Ä(θ )θ = [ ] [ ] [ ¼, ¼ =, = Ä(θ )θ ] [ ] À, À =, À ]. ½» ½
31 ÊÑÖ ÈÖÓÓ ÓÙÒ ÓÚÖÒ Ì ÔÖ ÒØ Ö ÙÐØ Ò ÔØ ØÓ Ø ÓÚÖÒ¹ÓÒ ØÖÒ Ò P.Ø. E{P, ½} P ¼, P ¼, Ì Á, Ö È π Γ, =¼ ÛÖ Γ ÓÒÐ ÑØÖÜ ÒÓØÒ Ø ÓÚÖÒ ÓÒØÖÒغ ¾¼» ½
32 ÊÑÖ ÈÖÓÓ ÁÒÜ ÊÑÖ ÈÖÓÓ ¾½» ½
33 ÊÑÖ ÈÖÓÓ ÈÖÓÓ ÓÙÒÒ Ö Ø ÐØ Ù ÓÛ Ø ÚÓÐÙØÓÒ Ó ÕÙÒ {G } ÛØ ÒØÐ ÚÐÙ G ¼ P ÛÖ G (,¼,...,,Ö )º Ä Ù ÒØÖÓÙ Ø ÚÖÐ Z (,¼,...,,Ö ) ÛØ, =, È º ÌÒ ÙØÖØÒ E{ P, ¼} P ¼ ÖÓÑ G ½ = E{G ¼, ¼} Û Ø ½, Ö =¼ Ô, π π ( + À ¼ )¼, ( + À ¼ ) Ì ½µ ÓÖ ÐÐ = ¼,...,Ö º Ì ÓÒÐÝ ÔÓ Ð ÓÔØÓÒ ÓÖ ½µ ØÓ ÓÐ ÚÒ ØØ G ¼ P ½, ¼ ØØ ÑÒ ½, È ½, Ò ØÖÓÖ G ½ Pº Ý ÒÙØÓÒ Û Ø ØØ Ø ÕÙÒ {G } ÓÙÒ Ý P ºº G P ÓÖ ÒÝ Ò ÒÝ ÙÒÖØÒØÝ ÙÐÐÐÒ Ì Á ÛÒ G ¼ Pº ¾½» ½
34 ÊÑÖ ÈÖÓÓ ÈÖÓÓ ÓÙÒÒ ËÓÒ ÐØ Ù ØÙÝ Ø ÚÓÐÙØÓÒ Ó ÕÙÒ {Q } ÛØ ÒØÐ ÚÐÙ Q ¼ P ÛÖ Q (É,¼,...,É,Ö )º P Ú Ø ÑÒÑÙÑ T { P} ØØ ÙÐÐÐ E{ P, ¼} P ¼ ÓÖ ÒÝ Q ¼ P Û Ú ØØ Q ½ = E{Q ¼, ¼} Q ¼º ÌÒ ÓÖ ÒÝ Q ½ P Û Ú Q = E{Q ½, ½ } Q ½. ÌÖÓÖ Ø ÕÙÒ {Q } ÒÓÒÒÖ Ò Ò ÛÒ Ø Û Ú ØØ Q P ÓÖ ÒÝ ÙÒÖØÒØÝ ÙÐÐÐÒ Ì Á º ¾¾» ½
35 ÊÑÖ ÈÖÓÓ ÈÖÓÓ ÓÙÒÒ ÒÐÐÝ ÐØ Ù ÔÖÓÚ ØØ ÓÖ ÒÝ P ¼ ¼ Ø ØÖØÓÒ P = E{P ½, ½ } ÓÙÒ Ý P ÓÖ ÒÝ Ì Á º ËÒ P ¼ Ò ÓÙÒ Ý ¼ P ¼ Q ¼ ÛØ Q ¼ = P ¼ + Pµ Û ÖÚ Ý ÒÙØÓÒ ØØ Ø ÚÒ Ò ØÒØ ½ ¼ P ½ Q ½ Pº ÒÒ G ½ Q ½ G ½ P ØÒ ¼ P ½ G ½. ÌÖÓÖ ÕÙÒ G ÐÛÝ ÓÙÒ Ý P ØÒ Ø ÕÙÒ {P } Ð Ó ÓÙÒ Ý P Ò Ø ÓÙÒÒ ÑÓÒ ØÖغ ¾» ½
36 ÊÑÖ ÈÖÓÓ ÈÖÓÓ ØÖØÐØÝ Á ÓÒ ØÖÒØ ÈÊ = Á ÓÐ Ø ÑÒ ØØ Ê = È ½ ÓÖ ÐÐ = ¼,..., Ö º ÔÔÐÝÒ ËÙÖ³ ÓÑÔÐÑÒØ ÓÚÖ È Ò Ø ÄÅÁ Ð ØÓ Ψ È ¼, = ¼,..., Ö ÛØ Ψ = Ö =¼ + π Ô, ( (È ½ Ì α ) Ì π Ö =¼ π ( Ô, Ï Ì + Î Ì π +α ½ ). ) Ì À À ÆÓØ ØØ ÑÙ Ø ËÙÖ³ ØÐ ÓÖ Ø ÕÙØÓÒ ØÓ Óк ¾» ½
37 ÊÑÖ ÈÖÓÓ ÈÖÓÓ ØÖØÐØÝ ÔÔÐÝÒ Ø ÒÕÙÐØÝ (+ )É(+ ) Ì (É ½ α Ì ) ½ Ì +α ½ ÀÀ Ì. ÓÒ Ø ÓÚ ÕÙØÓÒ Û Ø E (P, ½) È Ψ È ¼, = ¼,..., Ö, Ì Á. ¾» ½
F(jω) = a(jω p 1 )(jω p 2 ) Û Ö p i = b± b 2 4ac. ω c = Y X (jω) = 1. 6R 2 C 2 (jω) 2 +7RCjω+1. 1 (6jωRC+1)(jωRC+1) RC, 1. RC = p 1, p
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