《信息论与编码》傅祖芸_赵建中_课后答案

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ὅ!fgḄhiᨵ/=logl2+log2=log24&ᱯkᵨᜩ)5lᨵmnopឋBஹ#ஹrsmὅ!sᭆ᳛ḄᙳP=hiᜩ)u?]◀ḄYZឋ/=log3hi<=5Ḅ?ᦪ11H2.9?hlog3hi:;◤53?஺ூyz௃᝞}1@ᑖ3ᚮuᚮ43?1pᔲ167Ꮇ஺[2.2]lᡮᙳᒴḄ“,☢4ᦪ2”ᡈ“☢4ᦪ8”ᡈ“,☢4ᦪ!34”l89mnᑖ>;DE@A:“,ᦪ2”ᨵnopᓽ,Ḅᦪᔜ1,ᵫd
ὅ!fgḄ,

1hiLnOPḄᭆ᳛P=77,LMNḄDE:

2log36H5.17&ᱯ“,ᦪ8”ᐳᨵ᝞opB26ஹ35ஹ44ஹ53ஹ62,ᭆ᳛P=',hiLMNḄDEB6636/=log-H2.85&ᱯ5“,☢4ᦪ!34”Ḅopឋᨵ,nB34ஹ43,ᭆ᳛P=1—1',6618hiLMNḄDEB/=logl8H4.17&ᱯ[2.3]᝞ᙠ⍝ᜩ!¡Ḅ9Ḅ¢£“¤ᜩ¡@”ᑣ¦ᫀ¨ᨵ>;DE@᝞ᙠ©ᜩ!ªḄ«6᪵Ḅ9⚪ᑣ¦ᫀp>;DE(Ꮇ©:®Ḅ¯°)@AB᝞ᜩ²l³Ḅ´¦ᫀopᨵµnopឋun¶!sᭆ᳛ḄᙳP=hiilC¦ᫀḄDE/=log7=2.807&ᱯk©ᜩ²l³᪵Ḅ9⚪ᐸopឋᨵnᓽOPḄᭆ᳛1,ilḄDE0&ᱯ஺[2.4]·¸JᙢºḄ᝕¼ᨵ25%!ᜧ¾Pᙠ᝕ᜧ¾Pᨵ75%!¿À1.6ÁÂ4Ḅk᝕¼¿ÀL6ÁÂ4ḄᓰᦪÄ஺Ꮇ᝞ᡃÆ“¿ÀL6ÁÂ4ḄJ᝕¼!ᜧ¾P'’Ḅ]E9>;DE@A:A⊤É᝕¼!ᜧ¾PP(A)=0.25U

3B⊤É᝕¼¿À1.6ÁÂ4P(8|A)=0.75,P(B)=0.5“¿À1.6ÁÂ4ḄJ᝕¼!ᜧ¾P”ḄOPᭆ᳛••5
—••2=—

4ËÌὀBÎBÏ—©LMNᡠpḄDE/=log03U5HL415&ᱯIX]=042=143=23=3*1,ᐸO6Ḅ]E1/41/4(202120130213001203210110321010021032011223210),Ñ(1)i]EḄÒDE!>;@(2)ᙠi]E)ᙳuÓÔÕÖ×ḄDE!>;@ABDØ!ÙÚÛḄhiO6Ḅᔜ]E³!ÜrfgḄilO6Ḅ]EḄÒDEᓽᔜ]EḄÒDE஺᪷Þ©ᩩNO6ᔜ]Eᡠᒹ¨ḄDEᑖBO/(a°=0)=logB=L415&ᱯ/(ব=1)=log4=2&ᱯI(ai=2)=log4=2&ᱯI(=3)=log8=3&ᱯa}ᙠO6Ḅ]Eᐳᨵ14Ó“0”ÔÕ13Ó“1”ÔÕ12Ó“2”ÔÕ6Ó“3”ÔÕᑣᑮ]EḄÒDEB1=14-1.415+13-2+12-2+6-3H87.81&ᱯ45ÓÔÕᐳÖ×87.81&ᱯḄDE)ᙳuÓÔÕÖ×ḄDE/=Ì=1.95&ᱯ/ÔÕ45åæB]E)ᙳuÓÔÕÖ×ḄDEᨵdçᦣ)ᙳÙÚÛDØ)ᙳuÓÔÕÖ×ḄDEὅ!DEéoêë

5"(X)=

6[2.6]᝞ᨵ6î8ᑡḄðñ.òóᨵ
ÓôAB,ᑖÂsᭆ᳛õᐭ÷.òᑁ,ùúÆḄᙶ᪗ᑖ(XA,YA)(XB,YB)ABpõᐭ.òᑁ஺(1)óýᨵôA,ÑAõᐭ÷ÓòḄ)ᙳÒDE!>;@(2)ó©A©õᐭÑBõᐭḄ)ᙳÒDE஺(3)óAஹB!oᑖþḄÑAஹB¶õᐭḄ)ᙳÒDE஺AB(1)ÑôAõᐭ÷òḄ)ᙳÒDEᓽÑDEé✌ᐜ
AᐭḄᭆ᳛|P1=11148Iai<73&481111II48481"A]ᙳff(A)=log48=5.58ᱯ/(2)Aᐭ!"BᐭḄᙳ!ᓽ"H(8|A)஺”(8[A)=[<

7H(AB)=H(A)+H(B\A)=l\A3ᱯ/[2,7]/ᜧ123ᧇ⍝!ᵱឋ89:⁐<Ḅ=>᳛7%,᝕ឋ=>᳛0.5%,᝞ABCDᵱ-E“BGᔲG9:⁐

8ᵱ-E9:⁐<Ḅᭆ᳛:[X~\I6!l6Z21JJCᵱ-ELM“G”ᡠc᧤Ḅ/=log0H3.836ᱯ/Cᵱ-ELM“ᔲ”ᡠc
Ḅ/=log0mH0105ᱯ/ᵱ-EᙳU)LM8RᨵḄ”(X)=[log6,Ḅ᩽ឋ஺X:H(X)=[log6

9GḄᭆ᳛ḄᜓOᱯឋ!᩽ᩩ+஺IP1=10.070.9310.0050.995Jூ2.8||=|0.20.190.180.170.160.171,"Ḅ,X

10[2.9]ᦣSᐸA=m!G,...,a,},ᐸ£¤Ḅᭆ᳛ᑖ¦(Pi,R,…!ª)o«ᦣS2,ᐸSḄP¬!A2-{a,,i-1,2,...,2^},®ᔜḄᭆ᳛ᑖ¯P2=(l!N)P,i=P,2=XP=1(1IN)P2o¾¿p\2-p\1X!p2z=Q+W!ᐸ80<2W6pJp2,ÂᐸKᭆ᳛Ã஺±ÄÅᵫᡠ
ÇḄᭆ᳛ḄGÈÉḄ!ᵨḄᱥᳮÍÎÉÏX஺XÇḄX2,ÇḄ:"ÐX2Ñ=]

11LP1P21ீ2J/2(i)=log
50piIx/(x)=(piIx)log(pi1x)+(0+x)log(pi+x),x0,1I,ᑣ

12ᓽØᦪ/(x)ÚØᦪ!ᨵ/(O)e/(Z)ᓽ(pi127)log(pi1N)+(22+0log(/?2+J7)5pilogpi+p210gpi஻(X)3஻(X2)ᡂÞ஺ூX௃ßḄᭆ᳛àᔣâᭆ᳛ᑖ¯.!ãឋÈÉ!ᓽGÈÉḄ஺qH(p,p2…pm,qiq?,qQ=H(pஹ%&,…pm,pL)+pLH(,,,!஻)PLPLPLäÅâåḄᱥᳮÍÎ஺XH,pi,q\,qiq.)n=1pilogpiIp210gp21...IpL\\logpLnIq\logq\1qilog<72I...Iq,logqnm=1p\logp\IP210gp21...1PLWlogPLWIPLlogPL+pLlogpL1q\logq\1qilogqi\...1q,nlogq>n=1p\logp\IpilogpiJ...1PLlilogPLW[J)LlogpL+ভ+[2+0+••+q,)logPLn1q\logq\1q210gqiI...Iq,logq,”n=Ip\logp\IP210gp21...1PLWlogptn[PL\ogpL"logéqqpi.pLPL=1p\logp\IP2logpi1...1PL\\logPLn[PLlogPL+PM!qஹqqqqqPLpLpLpi.pi.pi.q=H(pi%2,%0,…,M)pi.PLpi.ூÍÎ௃ê8ëìíᑖᒘ!ÂᑖᒘïḄᭆ᳛ð,âñòᑖᒘḄḄᭆ᳛!ᑣÇḄóÈÉ!óᡠÈÉḄ•⚗öGᵫñᑖᒘÂ÷øḄãឋ஺

13[2,12](1)ùúᵯüýþc
ÿḄᨎḄ〉Ḅ◤⌕ᵨ5x105ூ2.11]஻,=1,pz.,ᑣᐜ—Iqilog-r4...1q»log/n—t----logT-J2log2I—ߟ,[mlog-nr)----

1410!"#ᵯ%&'⌴)*ᡠ◤Ḅ,-᳛(ᱯ/2)஺5672⌕'〈309*ᡠᨵ;<=>ᓄḄ@ᡠᨵ#ᵯ%Aᭆ᳛CD஺(2)6EFᵯGH◀JKLMNOᵯPGHḄQR⌕&᜜TUVᨵ30!"Ḅ⁐F'XYF⁐GHḄ,-᳛⌕NOGHḄ,-᳛Zᜧ2.5\%^7Ḅᵯ%_`10!"Ḅᵯ%7abᡂḄᭆ᳛defIy'ெQI஻2,6fio1|/>|=11fI101Y᪵%ᙳ7jkḄ,-lfH(X)=loglO=3.32ᱯ/DᙠᡠᨵḄnoe<=>ᓄḄp)79*qᨵḄ,-lfH(XN)=NH(X)=5-10s-Iogl0=1.66-10,ᱯ/9(ᢥ72'X309st72◤⌕'XḄᱯᦪᓽ,-'X᳛f30H(X,v)=4.98-107ᱯ/2◀KLNOᵯPGHḄ⌕&᜜T◤30!"Ḅ⁐F!w67⁐FAᭆ᳛CDᑣᐸᭆ᳛deflylb\bl…{301IPI=11y301"1ᐸ|flog30ᱯ/}~ᵫMᵯ%⁐F;<=Ḅp)ᨵ“(xy)=”(x)+”()=log300Y᪵F⁐ᵯPGHḄ,-᳛NOᵯPGH,-᳛ḄfHH(XY)

15X)log300H2.5log101010J3030J

16[2.13]79ᵯP*f;ᵫ3x105ᡂᡠᙳ;<=>ᓄ@7a_128!"Ḅ#ᵯ%56#ᵯ%Aᭆ᳛CD஺79*qᨵ,-l?DᨵaᕒᙠZ10000Ḅ⌱1000ᩭ¡R)ᵯP*ᕒ¢R)*ᡠḄ,-l;£Ꮇ6;Aᭆ᳛ᑖ¦5@§)¨©ª«¬⌕ាᙢ¢R)*ᕒᙠ¡R¯◤ᵨ¬^7Ḅᵯ%#bᡂJaᭆ᳛de᝞±1x1ஹQ122…Q128|IPI=%ᙳ7jkḄ,-lf”£X«=logl28=7ᱯ/79*ᵫ3x105ᡂ@e;<=Ḅp)79*qᨵḄ,-lfHX
=NHX
=2.I-106ᱯ/9N᝞ºᵨᩭ¢R)*%ᙳ7jkḄ,-lf//£r«=logl0000=13.29ᱯ/⌱½1000ᩭ¢RjkḄ,-lfH£y..v=NH3Y=1.32910aᱯ᝞º⌕ាḄ¢R)*ᓽ,-!ÁᜫᙠQRᎷ6!>ḄÃı◤⌕Ḅᦪf//(%>■)2.1106H1.58-1013.295H(Y)[2,14]fJ'XaᵫÈAஹBஹCDᡂḄ}~Ì,Í7ÈÎṹᡂÐÑᐗṹᾭÔÕᑡ00×⊤A,01×⊤B,10×⊤C,11×⊤Do7ÑᐗṹᾭÔÚf5mso

17(1)!"ÈAᭆ᳛CDÝst'XḄ%ᙳ,-Þ᳛?128128128J

18(2)7ÈCDḄᭆ᳛ᑖßfp.=1,PB=pc==,“)st'XḄ%ᙳÞ᳛¬^Ꮇ6!"ÈAᭆ᳛CDÝ%ᙳ7}~jkḄ,-lf//(X)=log4=2ᱯ7ÑᐗṹÚf5ms,7È◤⌕2Ñᐗṹᑣᐸ'XÝef10ms,72'〈n=100p),-'XÞ᳛fR=஻"(X)=1002=200ᱯ/2!"Èᭆ᳛!"Ý%ᙳ'X7ÈjkḄ,-lf--------7---------2,«log-=1.985ᱯ/}~344II)J)Ý'XḄ%ᙳ,-ÞfR=nH(X)=1.985•10ᱯ/22[2,15]àᦣ%â,ãᨵ“(X3|XIX2)6”(X2|XI),äAåᡂ=Ḅᩩç஺^“(X3|XiXz)=[<<◄P(X.X2)logP(X3IX!X2)=1<

19:H(X)=log5+log4+log4+

20”(XiXz…X,v)="(Xi)+“(X2|Xi)+…+”(X,v|XiX2…XNH)õ”(X,V|XlX2…X,vh)XlX2XN=<…?@ᨵḄᡠᨵ,-஺

21C:)i(10g)(.trnftL<<<(2)3;)(4H)|(2BXXXHL)(limXHN.

22P-R(20T1Ḅᭆ᳛VᐵX689ḄᓽP6Zᦣ89஺ᐸ]^”(X)=[?@Ḅ,-6ᡠᨵ4yz{ᑴᦪḄ᣸ᓽ0000-1111ᐳ16,-஺[2.18]ᨵᙠ&P(a)=0.6,P(b)=0.3,P(c)=0.1Ḅᭆ᳛(2X᝞1133᝞Xi^cᑣX?^aஹbḄᭆ᳛^^cḄᭆ᳛^0஺"#☢(2X9Ḅᭆ᳛VX/Hᨵᐵ/e3P(X,|Xm)=P(X2|Xi)஺3ᵨḄ2᝱<;Ḅ]HoC^▤ᐸ᝱ᣚ᝞£ᡠ஺a'":;3,1b:31b:"31i13212C3᪷¦§¨᝱ᣚ᝱᩽▲ᭆ᳛ᑖ¬^(஺)ஹP(b)TP©,᪷¦ᑗ¯°ߟ²

23³´µ¶·ᨵlimHN(X)=lim——Xi^aᑣX2^aஹbஹcḄᭆ᳛^᝞^bᑣXz^aஹbஹcḄᭆ᳛^

241!133211|஺(0+஺º+஺3)=1C¸:31஺ভ=¼=0(c)=½o4¸▤Ḅ]^:H=¾஺(E)"(X|E,)=1.439kᱯ/,-PP2[2.19]--▤Ḅ᝱᝞Àᡠ,0P.PXḄ,-Á^Â0,1,2Ã<ÄÅp=l[po2P(1)Ç89Ḅᭆ᳛ᑖÈP(0)ஹপ஺22T2222)½2P(2)ÇḄÊH½(3)ËÌÍ^^no,-Ḅᭆ᳛ᑖÈÎ89ᑖÈ஺ÇËÌḄ]"(X)

2522f03)=3஺ভ+303)+2Q(c)Q(b)=Q(a)+Q®+Q(c)|Q(c)=Q(a)+Q(b)f(3p(0)=pP(O)+1?(1)+TP(2)Úপ=-P(0)+Ûপ+-|P(2)=-P(O)+-P(1)+Üᡝ(2)IP(0)+P(l)+P(2)=1

26C¸P
0=P
l=P
2=13——P▤Ḅ]^H=p=HãᑮᨬᜧÕᨬᜧÕ^log3=1.585kᱯ/,-஺p=0H=0kᱯ/,-½஻=1H=1kᱯ/,-ூ2.20]æçèéêëḄᨵæ⁐Tç⁐íᓽX=Âæ,çÃ,æ⁐2îḄᭆ᳛^PÞæâ=0.3,ç⁐2îḄᭆ᳛^P
çâ=0.7oÞ1âᎷ§æç2î'ðᨵᐵὶÇ]"ÞX½Þ2Ꮇ'ᨵᐵὶᐸᐵò^PÞç|çâ=0.9,PÞæ|çâ=0.1,PÞç|æâ=0.2,Þæ]æâ=0.8,Ç▤Ḅ]Hzo
3ᑖ¬Ç§¨íḄᑍôõ

27æçí᝱Ḅ᩽▲ᭆ᳛^᝞æââ=þ2஺Þ.ÿ+,0ߟ:f=0.8Q
+0.1Q|0
+0
=12
1=;10
=;33Ḅ!"#H=$஺E,“
X|E=0.553&ᱯ/)*+Ḅᑍ-.ᑖ0#©i=lI=19©i=l[”=0.447log223⊤56Ḅ7!89ᨵ;<=>?@7!ḄABCឋEF஺GH⚪JK,6ᨵ;<=L☢NO⁐7!>Q☢RᜧTᦪVO@W⁐7!XL☢O⁐7!>Q☢YHZ[O⁐7!஺\=ḄᙳABCឋEF>ᡠ_7!89ᨵ;<=`ab7!89c;<=Ḅ`>\⊤5deOf᧜ḄᙳABCḄᜧa஺Jᒕ-.eOf᧜7!;<ᐵjḄkF>ᒕ-.lᜧ>7!89Ḅ;<ᐵjGlᜧ஺

28mnopQq⚪[3.1]r[x-|Ixixi~|sstuvw᡾⍝>zᦈ)*#|=[W>~],⍝⌴ᭆ᳛᝞ᡠ>
1XmX2ᑖ0ᨵḄ!XXI5/62ᦈᑮ7!j=l,2Q>Ḅᐵbx
z=l,2Ḅ1/6n3/4sஹ>1/4
3xyḄ!dX4⍝ᶧ.஻X||dH3Y\XX5zᦈᑮ7!|QḄᙳ!஺(1)XX,X2ᑖ0ᨵḄ!ᑖ0#/(n)=logp=Ilog0.6=0.737&ᱯ/(i2)=logp(X=Ilog0.4=1.32&ᱯ(2)᪷CḄ⍝_¡?ᐭᭆ᳛ᑖ£>P(y)=

290.059&ᱯ\p3x
\=|0.60.4|▼

30P(WX2)=log77=10g%=10.093&ᱯ/(i2Xyi)=logP(y)U.O10P(.Mxi)=logª=log=[0.263&ᱯ/(»*)=logPMP(V2g1/4/(M;ᡝ)=log=log¬=log=0.322&ᱯP(y2)3x_¡yḄd#:"(X)=[<¤(x)logP(x)=[0.6log0.610.4log0.4=0.971&ᱯ/)*X”(y)=[

31/xXy=//xI|y=0.0075&ᱯ/)*//(XIy)=10.6tlog+logIi0.41log+log1=0.9635&ᱯ/)*=10.6Hog+log|[0.41log+logI

32[3.2]r8·¸ᭆ᳛ᑖ£Ḅ7!tu⌴ᭆ᳛#pḄBSC¹º〈>8·7!¼½ᡂ¿ṹÁM¤0000,M2=0101,M3=0110,M4=0011M=1001,M6=1010,M7=1100,M=llll58ÂÃ(1)zᦈᑮmv·ᦪÁ0ÄMl89Ḅ!X(2)zᦈᑮmÅ·ᦪÁÆO0=>ᑮTÇᐵbMlḄ▬É!;(3)zᦈᑮmn·ᦪÁÊ#0=>ËÌÉÍTÇᐵbM>Ḅ!;(4)zᦈᑮmηᦪÁÏO0=>ÐÌÉÍTÇᐵbM1Ḅ!஺ᔜ·)*ḄᐜÓᭆ᳛ᙳ#8—(1)᪷NÔᩩ>ᨵP(yi=0|Af1)=P(yi=0|0000)=F(yi=0|xi=0)=p/1p(y=0)=QP(M,)P(0|M,)=;Mi-Õzᦈᑮmv·ᦪÁ0ÄMl89Ḅ!Öv1=0)=logP("="%)_|gP=i+[ogp&ᱯOP(yi=0)1/2(2)᪷NÔᩩ,ᨵP(×m=00|Mτ)=P(9y2=00|0000)=p2p(y"=00)=ᑮTÇᐵbM.Ḅ!#:

33/(MiX)”2=00)=log"(Þ=஺஺τR=log=2+2log>&ᱯ/)*r(yiy2=00)/4ᑮḄ▬É!#/(Mi;ᑶA=00)1/(MiXy=0)=1+logp&ᱯ/)*(3)᪷NÔᩩ>ᨵP(y\yiᑶ=000|Mi)=P(yy2y3=000|000)=஻3P(y,yy=000)=4P[M,)P(000|M,)=L+3pp2+3p?p+pJ=23MiÕzᦈᑮmn·ᦪÁÆO0=>ᑮTÇᐵbᯅḄ!#......aIää=000å1).p>cinnn/(Mwy2y3=000)=log=log=3+31ogpP(yiy>2yy=000)1/6=ᑮḄ▬É!#I(MiXy\yiᑶ=000)[/(MI;VV=00)=1+logp&ᱯ/)*(4)᪷NÔᩩ>ᨵP(yiy2y3y4=0000|Mi)=P(yiy2y3y4=0000|0000)=P(y,yy,=0000)=4P[M,)P(0000|M,)=][p4+6pp+p>]2MiÕzᦈᑮmη)*#0=>ᑮḄᐵbM-Ḅ!#....nnnn\iv¥¥25=ë)MMy.)-2)>3=0000)=log-46/vᓝXP(yiy2y3y4=0000)vpa(vv18=3+4logpIlogp4+6p2P2+p$)=ᑮḄ▬É!#I(AfiX)!iy2y3y4=000)I/(Miy2y3=000)=logpIlog(/X4+6pz+pt

34[3.3]rÅᐗîï⍝Ḅ⌴ð▣B1233J(1)ôP(0)=3/4,P(1)=1/4,H(X),H(X\Y),H(Y\X)/(X;Y)X2ù⍝Ḅ⍝ú©¡ᐸüᑮ⍝ú©=Ḅ?ᐭᭆ᳛ᑖ£஺:(1)᪷NÔᩩ>ᨵtt=1logIlog஻(X)=[

35”(XIy)=[⍝@AB>⍝C=ᐸ>⍝EFGH2133᪷JAB>⍝ḄឋMNOPp(0)=p(i)=:R>⍝ḄST᳛/(Xy)Vᑮ>⍝EF஺[3.4]Yᨵ[ᢇᵯ^ᢥ^`ᑖ70%@2kC,30%@5kQᢥbὑᑖ64%@1/8W,ᐸd@1/4W஺efO2kQ^`Ḅᵯ^g80%@1/8W஺,hijF^`NklᙳnᑮḄᐵpqᦪḄ>sF@tuv*H᪷JfOᩩxYᵯ^Ḅ^`GyxX,ᵯ^ḄbὑGyxY,ᑣ{yxḄᭆ᳛}~GHIX1Ixi=2k&X2=5k&]Irlly,=1/8W*=1/4]0.70.30.640.36ᩩxGP(y|xi)=0.8,P(”I")=0.2,t0.64=P(p)=P(xi)P(yR)+P(X2)P(y“X2)=0.7*0.8+0.3*P(ᵨ)0.36=(»)=P(r))(yz|)+P(X2)P(y21)=0.7*0.2+0.3*P(.|%)*nHP(yg)=>P(*|x2)=]

36/>xy?=H>y?I”>y|x?=o/86ᱯ/=1flog+logIIflog+logIC=11H(p)=1IH(,)=0.082ᱯ/|P|=II,|P|=I//(y|X)=lo.7*(0.8log0.8+0.2log0.2)10.3*f——+1=0.7567

373,5Xஹyz@FH1zx)yz=zx)r+zx)z|y=/x)z+zx)y|z2/x)y|z=/y)x|z="x|z"x|yz3/x)yizeoP3Px,z,y@Rᡂ¢஺H(1)z)logff(xlvz)1/(X;YZ)=P(x,y,z)k)gp(x)'LP(x|yz)P(xIy)ஹxyz

38I/(X;Y|Z)=y|z?=P>y|xz?ᓽ>X,Z,Y?@஺[3,6]ᨵ¼ᦣFᨵ᝞¿ᐵÀHX+Y=zᐸgxyÁÂÃÄÅ¢H>1?">X?6”>Z?,P3PY@ÆFRᡂ¢)>2?H>y?5H>Z?,P3PXGÆFRᡂ¢)>3?஻z?6”>xy?6”>x?+஻y?,P3Px,YgÇÈ[GÆFRᡂ¢)>4?/>xz?=஻z?I஻É)>5?/>XY;Z?=H>Z?>6?/>xyz?=">x?>7?/Éz|x?=">y?>8?/>xy|z?=஻x|z?=">y|z?஺X+Y=ZRᨵP>z|xy?=J,ᓽ">Z|XY?=011z=x+yH(Z\XY)=H(Z)lI(XY;Z),CÊᓃ/(XY;Z)="(Z)஺

39H(Z\X)=l4p(x,z)logP(z\x)P(x,z)P(x)P(x,y)=1sḄឋMᨵ/>xz?£0,C=஻z?£஻y?ᡂ¢PxGÆFRZXḄᭆ᳛ᑖÌÁC=-ÍÎgḄᡂ¢஺ᳮHZ
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[Ö×ØÄÙ:(1)"(X),//(7),H(Z)9(2)H(XY),H(XZ),H(YZ),H(XYZ)(3)H(X\Y),"(X|Z),”(Y|Z),"Ú|X),H(Z\Y)

40(4)H(X\YZ),H(Y\XZ),H(Z\XY)=!

415/x)y/x)zzr)z)(6)/(X)y|Z),l(Y;X\Z),I(Z;X\Y),I(Z;Y\X))(7)/(xy)z),/(x)rz),/(y)xz))ᵫpxy@ÁÂÅ¢Ḅᭆ᳛ᑖÌḄFC=ᨵHx="y=iᱯ/lo1-1,C=P4U3144H(XY)=H(X)+H(Y)=2ᱯ/᪷JfOᩩxNnP(x=0,z=0)=ᡝ(x=0)=»P(x=O,z=1)=0P(x=l,z=O)=P(x=l,y=O)=1,P(x=l,z=l)=P(x=l,y=l)=-P(2=1,X=O)1,P(z=l|x=O)=(X=0)▲=0,x=1)P(z=l,x=1)P(z=l|x=l)=P(x=1)H=0.5ᱯ/2424HXZ="X+HZ|X=1.5ᱯ/ᳮ"z|y=o.5ᱯ/”yz="y+"z|y=1.5ᱯ/,C=HZ\XY=Oᱯ/H(XYZ)="(XV)+“(ZIXY)=2ᱯ/

42H(X\Y)=H(XY)IH(y)=1ᱯ/zḄᭆ᳛}~G:Eh."(Z)="(,)=0.811ᱯ/H(Z|X)=I

43஻X|Z="XZl஻Z=0.689ᱯ/H3Y\Z=H3YZJH3Z=0.689ᱯ/"x|yz="XYZI”yz=21.5=o.5ᱯ/ᳮHy|XZ=0.5ᱯ//x)y="x”x|y=oᱯ//X;Z="X”X|Z=0.311ᱯ//y)z="y1"y|z=0.311ᱯ//X)y|Z=஻X|Z஻X|yZ=0.689I0.5=0.189ᱯ//r)x|z=zx)y|z=o.i89ᱯ/I3Z;X\Y=H3Z\YlH3Z\XY=0.5ᱯ//Z*|X="Z|XIH3Z\XY=0.5ᱯ/I3XY,Z=H3ZI”ZIXV=0.811ᱯ/zx)rz=HxIHX|rz=1!0.5=0.5ᱯ//y)xz=”r1“y|xz=o.5ᱯ/3.8ᨵ[Ðᐗ>⍝ᐸ>⍝᝞àáᡠã஺Yä>⍝k1500Ðᐗ/åḄæçSTTᐭeᨵ[ésêᑡᐳᨵ14000ÐᐗíYᙠïésg10.981p(0)=/>(1)=,ñ>sSTḄòçᩭὃ⇋10åᑁ÷ᔲùïésêᑡúᜫüᙢS〈ÿ஺
:

44⍝Ḅ⍝▣II,⍝:[0,980.0210.020.98JC=log21H(0.98,0.02)=0.8586ᱯ/10ᑁḄᨬᜧ15000.858610=1.288104ᱯ14000ᡠᨵḄ14000ᱯ"#$%Ḅ&'ᩭὃ⇋,10,ᑁ-./01140002஺[3,9]345_ᵨ6
6⍝Ḅ⍝▣ᑖ8᝞4:I111113I363111I16236363J|j11G=log41"(,,,)=0.081V'6ᱯ/;<="6⍝ᙳ?@A⍝"⍝ᑖ8Cz=log31"
"]]0.126ᱯ/r3636111263ᐭḄᨬEᑖF?Gᭆ᳛ᑖF஺[3,10]34ᑡ6⍝Ḅ⍝"KLM

45IpIT\X2N1[\XP\X2Z01PPপτPIT221NফIpl202WU
O6⍝ᙳ?P@A⍝"QᐭGᭆ᳛R"SᙳTUᑮ⍝"ᐹX᝞4:(1)P@A⍝Ḅ⍝Cl=max{H(y)}!H(p12\p1Z'ZZ')112£1[2W1Ii2Zlog22'l"(pIN,pIW,2N)210g2210g2=(1121)log+(P1W)log(pIW)+(PIW)log(pI27)1121(2)P@A⍝Ḅ⍝Ci=max{H(Y)}I"(pIN,pI£2N)N2£LN.2Z_Lெ_1Zlog^lNlogWlH(p1Z,pIw,2»loglog232262=(1!23)log[+(p1N)log(p\Z)+(p\Z)log(p127)+2271122=G+2N[3,11]345⍝Ḅ⍝\ᐸᨬEḄᐭᭆ᳛ᑖF"K3^£=0_Z=3RḄ⍝஺஺01011-£12
⍝Ḅ⍝▣᝞4110

46To^ol`wRpiti!JU,Io1IZ

47⍝ab@A⍝"cbP@A⍝"#$᪷e`f⍝Ḅghij"ᨵ

48(1I27)iiz,P(஻3)1+2(1I27)112-Q2>0R,C=log1+2(11227E)log3"⍝`I@⍝;1L6[3.12]H(X)?ᐭᭆ᳛ᑖFP(x)Ḅ0ᦪ஺஻(X)=P(x)logP(x)Xᙠ6ᭆ᳛ᑖFP(x)_2(x),᪗?⌕(H(P(x))+("(P2(X))6"((PI(X)+(P(x))᝞4:(H(P(x))+("(P(x))l”((Pi(x)+(R(x))=[(

49PÌÍÎPÌLÎ…P“N
R"C=logff1+2fI11=log2.6(loge

50=//ṑÒÓᘀ(Õ)]"(YM|XM)=IXi->HSC2HSCn-4Q"=1R,┯ìᭆ᳛p=(l1(1I2p))ᡂóÚᎷn=kᡂó"ᓽkæõ⍝Ḅ┯ìᭆ᳛[11(1l2p)]Út212Q஻=ᦇ+1R"ᐸ┯ìᭆ᳛

51^[11(1I2p)d+pll1[11(1l2p)]|(T_L_LT2-42_Jp-P(l[2p)*+p[[11(H2p)*]TIn1p[2p)«+p(lI2p)i.1--(l[2p).+Ú(l[2p)«2<—0>1I2p)“i]-C2M"ü⍝▣I2$R-ýᐭþᑖli71Q஻R"┯ìᭆ᳛ÿ
:'21|lim/(X஺;X.)=”(X”)[H(X.|X஺)=1[(|=0ᱯ/ᙳ
!ᭆ᳛ᑖ஺ᐸ&'(
)*+,-.'⍝ḄᐭX2{m,G,G,G}7!ᭆ᳛ᑖ8/(X;Z:/(x?@஺A)0Io11BCDḄ'⍝:EF
)-=1olo0101I[00011looof001110011°loll-oo11-oo1,001122||221!-L1.o°IOUIo0ioJ12200l

52=[P®)P(C)P(G)P(G)]11looo11I0?Olli[P(4)P(bi)P(b,)PR)]I0?P>G?P>G?P>G?][0I(X;Y)=H(Y)IH(Y\x\~1111111111111188884422422422=HAWloFfiogIlogI.logI-loglo01olr1|010|[P(a)P(C2)P(c)P(a)]oOil3I11|22°°l8824|J/(X;Z)=஻(Z)l”(Z|X)1111111111111188884422422422=1.5ᱯ/XY,/Zx

53,^_`Da⚪[4.1]+ᨵ-defghiᐸjkᾙ/m■oᨵᓝPZxdx=l,q8rstuivw஺ᐸxyA:h(X)=I+p(x)logp[x)dx=1+AcosxlogAdxI+Acosxlogcosxdx=IAlogAsinx[+4cosxlogcosxdx2z12AlogAI+♦COSxlogcosxdx{v=logc+ln(l+sinx)+ln(lIsinx)dsinx+cosxlogcosxdx=loge+In1Isin2Msinx.=Ίe+ln(l+sinx)dsinx+loge+ln(lIsinx)dsinx1_______________________12B-1+sin1+ln(l+sinx)dsinx=(1+sinx)ln(l+sinx)2_||~zdsinx11IdillA=2In2I2-=1(1Isinx)ln(lIsinx)1+ln(lIsinx)dsinx=1+ln(l[sinx)d(1[sinx)=2In2!2ᨵ

54A2[2AlogA+2Aloge\2AlogeIn2=12AlogA+2Aloge12A{+?p(x)?=1,ᓽA=2'[4.2]defghiXḄ(1)ᢣᦪᭆ᳛ᦪp(x)=/eSx£0">0",[0h(X)=I+p(x)logp(x)dx=l+/elogLeQdx=I+Ze"JogLdxI+Ze"Jogegdx="°gI,ᵫo+loge+Ine\LdeuXx=Ilog/4-logetInrioIloge+dt=Ilog/+loge=log7h(X)=1+p(x)logp(x)dx=log2+log

55)(2)⚪Cᵨ(1)Ḅ஺(X)=12AlogAIloge(2In2I2+2In2I2)2/i(X)=Ilog+logeI1=1+logeI1=loge(2)ᭆ᳛ᦪp(x)=Le11z+Le"logLe"=l+/elog^i/xdx1=l+/e\ixlogI+Le\LxlogLeIAdx

56[4.3]+ᨵ-defghiᐸᭆ᳛ᦪ
:ுbxi08x5afᐸx0q8rfghiḄ஺oH=X+K(K>0)Yi=2Xqᑖ8Ki:Y1ḄMh(Yx):h(Yi)oA)(X)=I+p(x)logp(x)dx22393ᵫ+p(x)dx=l,°3ᓃ=3,23yH=X+K(K>0)¡1=11ᓃ23ᓃ=2X¡¢M2123232[4.4]+£¤¥fghiXi:X2,¦§Ḅὶᔠᭆ᳛
IXI2+X22P(XiXi)=e2I

57=Xi+X2¯7-.°ᑖḄfghiᐸᙳ
0,±
2,ᓽPZ²\zJ=1+/?²2logbx2dx=Ilog/?12/?loge+%2Inxdxabloge\ayblogaIlogb//(X)=loge+loga1log3h(Y\)=/i(X)IE[logl]=A(X)=loge+logaIlog3/z(y)=/z(X)IE[log]=A(X)=loge+logalog

58p(X\X2)=C42ᐸ«
1122[4.5]+-de¼(½¾¿ÀᜧᘤÃÀᜧᘤḄᨬᜧÅ¡ᵯÇb,ᨬÈÅ¡ᵯÇ
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F,ᑣÚ᪵᳛
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2FlogSIa)ᱯ/æ[4.6]ᨵ-'çèឤ¤ÔêëìíḄᾭïíᜐᙠm:জò×'çdó¿'⍝'⍝CᦈCᦈᾭïḄíyᜐᙠ8:õò×஺ö÷fghiX:øḄὶᔠᭆ᳛ᦪ,ஹ1p(xy)=..(021a\)(biI&i)qh(X),h(Y),h(XY):/(X

59aiia\/i(K)=log2Cyi=log4+

60ìᳮp(y)=஻(X)=1+p(x)logp(x)dx=log(t/2Ia\))=[+p(y)logp(y)dy=log(ü1b\)h(XY)=1+/?(x,y)logp(x,y)dxdy=log(a21<3i)+log(/?21Z?i)I(X;Y)=h(X)+h(Y)Ih(XY)=0[4.7]ᙠde'çÊ᪷Þ«ஹᩩÿ
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Ḅ(1)/i(x|r)8/i(x),xyᡂ"(2)h(X\Xz…XM)3/I(XI)+/Z(X2)+■■■+h(X),XஹXi…XN$%N&ᡂ஺((1)h(XY)=I+p(y)dy+p(x|y)logp(x|y}dx31+p(y)dy+/?(x|y)logp(x)dx=I+Mx,y)logp(x)dxdy=MX)ᡂp(x|y)=p(x),ᓽp(x,y)-/?(x)p(y),4%X6ᡂ஺(2)᪷8ᩩ:ᭆ᳛=>Ḅ?ᐵA&ᨵC(XiX?XN)=஻(Xi)+/?(X?IXi)+஻(X3IXiX?)+…+6(XNIXiXzX.vh)᪷8(1)ḄKLᩩ:
MN
4%ᨵh(X1X2…XN)3/z(X1)+/?(X2)+…+/?(XN)

61ᡂ

62p(Xi\x\)=P(X2)p(X3IXlX2)=MX3)/?(XNIX\X2•••XNll)=/?(XN)ᓽp(XlX2)=p(Xl)/?(X2)p(X\X2X3)=p(Xi)P(X2)p(Xi)p(XiX2••XN)=/?(XI)p(X2)•••p(Xv)[4.8]OPQRSTUX,VWXEO,ᐸYᙳ[\▲ᓽᦪ_`abA,cdᙠ%ᩩ:fghḄᨬᜧ
Ḅᨬkᑖmndoᨬᜧ
஺p(qᩩ:᝞f(+p(x)dx=1+xp(x)dx=As᪗(d1+p(x)logp(x)dxḄᨬᜧ[஺᪀⌼wᦪF(p(x))=[+p{x)logp(x)dx+/+p(x)dx+xp(x)dxx+(Ip(1)logp(x)+/p(x)+▭p(x))dxz{=0,|◤"“""g"+~xp('))=0ᓽ4%ᨵdp(x)dp(x)Ilogp(x)Iloge+/+8*=0

63P3X?=2/+Iloge

64᪷8+p(x)dx=1,+xp(x)dx=A,h/+«xllogfdx=\®oc=I2/Hoge124%p(x)=:%A/?(%)=!+p(x)logp(x)dxLlீA)[4.9]NPQRSᑡX1X2…Xa,ᨵᭆ᳛=>p(XiX?…X”)E[(X,=m)]=4஺(RSᑡḄᑖUᔜᑮ᝱ᑖmn$%
ᨬᜧ஺ᨬᜧ
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ᨬᜧb1/h(XM)=~log2e-24%ᑡ
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bN

65+xp(x)dx=A®oc=JA(loge)(Ὴ12:´'”=1logf(loge)2ஹ|+(k)ge)2log2e/i2+log2e&+•+log12e(/12/i2•••/L2)Ilog4(hi1a.)

66:h3XiX2…XN·3஻¸Xτ·+C¸X2·+…+஻¸Xz·ᡂᔜᑖU஺¢£N¤¥¦§ᑖU¢¨¯>ᑖ°\▲b¹4]ᙳᒴᑖmḄ
ᨬᜧb//(Xi)=logº/a)4%ᑡ²Ḅᨬᜧ[b(h(X\Xi…XN)=log(>[0)+log.[A)+…+log(fev[av)Ni=l[4.11]OX\X2…XN»¼½?Ḅ᝱ᑖmḄRSTUᐸ¾ᑖ°bZL,,ᙳ[ᑖ°bm\,m2,•••,mNocY=X\4-X2+•••+XN¿¼᝱RSTUᐸᙳ[bm=4m.,¾\=7^(OXiX?¼?½Ḅ᝱ᑖmḄRSTUᐸᙳ[bm.,¾b4oOYi=Xx+Xi,᪷8VWᩩ:ᨵX)=X)Yi=Xy+Xi4%ᨵ1X11CP(À,ஹ)=P(»,X2)Á1W1X11C1X2]X211=P(M,X?)0]=P>Xl,X2?=p>X??P>X2?

67=P(X\)p(y21Xi)log4(biIa)

684%ᨵ2f2/J2/f26JzRGA2-2ÃJ¢2ÅMÆ&RI"•'J\x\ini\)2p()?21iiiinM)i22%=i—22"஻---1---.2122222fr/i—É4+2MCL22lkf(2ll[CJ,{”().ini+AJ212AXi+2xi(AÏ21AwlÏτA)+(AÏi+/i2/L/LIYl[Ã/1lÏ162ஹr[IJ1A621fimJ+/1I2♦y2Ï2ஹ1=22Í-KÎ/Citv+^r+i!-n~)22(rfM)(yaIm\Imi)2}22

69I(yaIx\Iini)2Uii226J1ுi22Jrrf2fI)1L111ÕÖf\i+Cn1ு2rai222"/"I1*×)f4%L=Xl+X2¼ᙳ[bÏ+S2,¾b6+GḄ©ªᑖmØᳮᓃ=Xi+x?+x.,.......y=Xi+Xz+…+XMᙳb©ªᑖm4%y=Xi+x?+…+X.¼᝱RSTU,ᐸᙳ[bm=Ûῖ¾/=Û2[4.12]OÝPQÞ⍝ᐸᱯឋ᝞f:p(y|x)=¢âᐭTUxḄᭆ᳛=>wᦪbp

70x)=122,______å——2M)2____________.P(A)=+expjlI2cç(=""■,-expK---------(>'21mi1mi)(å(1)ÞëḄ
ᡊᓾ;1f\imiIf\iyiI(2)Yᙳ½Þïxðñ""|`bᓝóôp(expfl._(>'21m\Imi)2(+Ã).JilUhlUP(X)=1t2)—H-")ே2V2^]2S(^A)J+l(yIx)2/3f2-=eix/4<-=eix/4(e\xn»2(

71ûXbᙳ[b0,¾b2/2Ḅ᝱ᑖmᐸ
bC(X)="log2e26="log4üJþÿ)1ுX2JI23/2I4(2361fU1>_4x+4y214xy1236fJ>2iJ112/4yl23/2exp)\2!IfIJ2]11;>236361fIJ¢112/22!\dx212fxlyl.rH21τ,…12(1>1/22f3dI2(বீJf>1212(2(y212:2(4%r¼ᙳ[bo,26Ḅᑖᐸᩩ

72ni2)I!^exp"126>L"H~yl஺p(y)=+p(x,y)dx=+2W(LI'iWi7e"+Ja=-e"+ee4(+eiidflog2e•2/2=log4e(i

73L'_1fyIx\dxdy=I+pU,y)log(3dxdyI+/)(A

74f!xI_1-,JP(x,y)\-------------te“dx+|yl2Ui—32—04(஺•1dxcly-edy362)3231I4+233=,;dx63(12(4(1xI22=log6(+loge^dxdyh(Y\X)=1B8§+loge+p(x,y)3621289CᙳEFG:=log4e(i1log3e(2(xy))[”(y|x)______1221423=0.21112IJK⚪MNOPQRᵨḄTUQWX:(2)+YJZ=2ஹ2[4.13]\]^_`abcdefgḄCᙳEFG/(%;7)hiᐭbcdeXḄᭆ᳛mnoᦪp(x)Ḅnqroᦪ஺]^:

75᧜dxdy/(X;Y)=+p(x)p(y|x)logp(y)p(y\x)+p(x)p()[x)logdxdy_p(x)p()[x)dxxyᙠXḄ_{ᭆ᳛mn:(x)|p“x),~ᦪ06(31,᪗]^:/((P(x)+(pi(x))e(J(pi(x))++(/(/?2(x))OP᝞J(/(pi(%))++(/(p?(x))I/(⊈(X)+(pi(x))p(y|x),,p(y|x),,=(+pi(x)p(y|x)logpi()+(+p“x)p(y|x)logপdxdyMW),,1+p(x)p(y|x)bgdxdyp(y)p(y)p(y)=(+pi(x)p(y|x)iogMHdxdy+(+p2(x)p(y|x)bg°পdxdyp(y),P(),)0,1=+pi(x,y)logM,dxdyt6log+pi(!,}■)dxdy=log+pi(x|y)p(y)dxdy=0ᳮ+p“x)p(y|x)log"dxdy60,89ᨵ?\)f/((pi(x)+(pz(x))e(/(pi(x))++(/(“2(x))[4.14]\]^`aF⍝Ḅᐙ⌕ᩩNF=1]^:(1)ᐙᑖឋ஺

76/?(y\yi•yN\x\xi•••xv)=p[y\\x\X2•XN)p(>21x\xi•••xvyi)•••p(yN\x\xi•••XNy\y2•)+p(x)p()Ix)logp(}')dxdyp(y|x)=4p(»l»)

77z.ஹ஻(xiᐗ2…XNyiV2…VN#IVN)p(yN|X}X2•••XNy\yiJMI)=p(X\X2•••XNy\yi•••).p(£y2•••y.11y“I•2••f.)p(y\yi••ywii|X1X2••XN)NIX)==li•••y/vnyNIx\X2••XN)dyN2NNiIXi)--<=l-i=l-NA/lliIXi)dyNjIXi)F=!Z=1=p(yw|xw)ᳮp(yN11IX]X2•••XNy\yi•••JA

7889ᨵ+pyyftpyIX?

79Nr=l[4.15]\]^`aF©XḄTªh(X)hᭆ᳛mnp(x)Ḅ«qroᦪ஺]^JxyᙠXḄ_{ᭆ᳛mn?(x)|:(X),~ᦪ06(31,᪗]^Jh((pi(x)+(pi(x))£(h(p\(%))++(//(pi(x))OP᝞J¬(p\(%))++(h(pi(x))Ih{(pi(x)+(:(x))=!(+/?i(x)logpi(x)dxI(+pz(x)logpi(x)dx++((pi(x)+(/)>(x))logp(x)dx,,Mx),,p(x),=(+/(x)logpM:+(+pMx)logHOdxP(x),p(x),',Slog+(x)pip1(l)=logl=0ᳮ+p“x)10gJx5089¬(pi(x))++(஻((x))1஻((pi(x)+(/?2(x))30[4.16]xF⍝iᐭh`aqbc®ᑡX\X°…XN,i°±h`aqbc®ᑡr.r-r,,F⍝²⌴ᭆ᳛mnp(y|x)஺\]^J2(1)´F©hµᨵ/(X1X2…X,vH%…ᓃv)£

80;(X1%2…XNKᓃ…ᓃV)6

81]^:Z(X1%2XNy»2-Kv)஻(X1X2…XNIyi)2…º)=+p(xa2•7.,»*•••yjv)logp(X\X2•••XN)p(yi32•yzIxiX2a)+p(X\X2XN,yi••y.N)logp(»/….)ஹP(½|»).(-2I\21•,.(XNIᡝ)=+/?(x\xi•••xv,yiyi•••yv)log/ஹ/\(ஹdx\axi•••dxNdy\dyi•••ayNp(Xi)p[X2)---/?(Xv)/MIXi)஻("I•-ÁXN)dx\dx2…dxNdy\dyi•••dy^=+p(xi-,»)"f)logp(y)p(y)…P(yv)(1)´F©µᓽp(XiX2…Xv)=p(Xi)p(X2)…p(Xz)ᓃ)k/(HX2…x,vy஻2…ᓃ)LP(MIW)P(X2IV?P(X,vIyN))

82Ñ••>')=஻(y௃)•஻(>')(1)(2)=+p(X1X2…Ôஹ',yiyi•••yv)f[log\\dx\•••djczdyi…dyz

83(1)X_Ë◀Ö(2)X_ËÐp(xi|yi)p(×21y2)•/?(×N|yz)=p(x\xi••XN|yi”…>N)89ÅÆᡂÈ´ÉÊ´`aF⍝஺(2)´F⍝µ,ᓽp(yi•••y.v|xiXN)=p(y|X[p(»|XN)µ/(XiXz……K)!

84PspF⍝ḄFõ÷30dB,gpiOlog.oPNPN89F⍝üeCPVýMÐóôP=2.71.107Hzlog1001[4.18]
ᙠᙳ᳛▲ឋ⍝⍝3kHz,
᳛+᳛!/᳛=10dB஺1!)*+,⍝-〈Ḅᨬᜧ2᳛ᓫ456!728᳛9:5dB,⌕=ᑮ?@Ḅᨬᜧ2-A᳛⍝BCDEF:1!᪷IJKᩩMᨵ,Ps+PN10login=10PNWXP=9ᑁLCீpj3=9.96103

85ᓽᨬᜧ2᳛9.9610,9ᱯ/`஺(2)᝞e᳛9:5dB,ᓽ10fghE"jI-W)0=10WXPNPN=Wloghl+o=2.710=Wlogffl+vH=3lOloglOP+PN

86=Wlogffl+-L-PஹCC=IWVllOo&gjliOopnIMog10=ᑮuvḄ2-A᳛WXBwᩭḄ2yᓽW=6IO3Hz

87z{|}~⚪ூ5.1௃ᢥP(0)=N1)=7Ḅᭆ᳛*Ḅᐗᑡ஺প)N஺N0.0530.01H(S)Ḅ஺(2))N=N஺5ᐺᑡG.ᨵḄᑡᦪ஺F:(1),ḄH(S)=

88(2)Nᐺᑡᑡᦪ±³µ°(1!rw)2,v[H(s)in

89C⌹ìṹWXṹCÖ•×ṹ7ṹDêÖ•×ṹWᐸâã~äî2P0)ABcDEFa\1/200000000ai1/400101101010100Cl31/16010Oil11011011001011/160110111111011101101110ï1/16100011111111010111110111஺61/1610101111111111011011111Oil

90ᔠᒹ0,®0ṹÚ7ṹEḄâã~äᔠñWXṹEÖÁ×ṹ7ṹFêÖÁ×ṹWᐸâã~äᔠᒹ0,®0ṹÚWXFêÖÁ×ṹ஺(2)ṹAஹCஹEᓽ5ṹ(ØÙ¥ṹ)(3)ṹAḄᙳṹ¥37ṹBḄᙳṹ¥2.1257ṹCḄᙳṹ¥2.1257ṹFḄᙳṹ¥2஺[53]ôõ¨ᳮ5.6,8öᙠÁṹ¥ḄÖÁ×ṹᑣÁ¨öᙠᐹᨵ?@ṹ¥Ḅᓽ5ṹ஺ôõ°᝞eöᙠṹ¥/.,/2ḄÖÁ×ṹᑣù/2,…஻À¨üý᝞Éê¤q81*=!᝞ṹ/2᪷Kraft᪀⌼ᓽṹḄ!᪀⌼"ṹ#Z.J2Ḅᓽṹᐹ)᪀⌼*+ᶍ-᯿/01ᐵ3ᳮ஺[5.4]:;;

91#(/,,/2,.)=(1,1,2,3,2,3)RrSḄT▲஺VWq/=1C1ni+nz+rn஺"Yr=2ᡂ[\Y/'=3ᡂ[஺^>_SḄT▲#3O◄rIP(s)1=Ip᝞⌕᪀⌼"ABCDṹᑣ1ᐵṹbcde,31,fᐭᨵ

92ூ5.5jᨵB;;<Ḅq"FG〈ᐭsBptᐗ;⍝vwxyq(Ꮇ:;⍝{|}|~Ḅ);⍝lmny⌴ptᐗFG஺;<*?ṹᔲ;⍝j*〉Y?ṹᔲvᙠ;⍝vwx|ᜫyqj᝞?ṹ^஺VW᝞*?ṹᓽ;⍝ḄpṹFGPQp;b⌼ᡂ;*?ṹ{|=;<;⍝஺;<ᙳlmo"Ḅ;#2.66*”(S)=12.66**?ṹ!§¨tὅḄ஺j⌕◤⌕P᡽¬;<Ḅ;

93(1)ᨬ±ḄtᐗDṹ{ᔲ{ᔲ{ABCṹ\(2)RvÅṹPQḄ;<ÆᑡḄᙳL.\(3)RvÅṹPQḄtᐗDṹṹÁḄᙳL2\(4)ÊËSÌ/L,VÍÎḄÏÐÊËÑÒÓ+?ṹḄ?ṹᦔ᳛;VW(1)¢ṹ{Ö×ṹ^>Ø3{A•Cṹ\(2)ᵫ;<0Û{|¸¹Ḅ^>ᔜ;;<ÆᑡḄᙳ#Ì=

94Ì=

95(4)=o.4756,åQælp;

96µê·/±ë⚪ூ6.1í:ᨵ•îᦣ;⍝ᐸ;⍝y⌴ð▣#:P(»)=P(x2)=P(x,)=:,ᑖóᢥᨬe┯öᭆ᳛÷ᑣᨬᜧøᯠCṹ÷ᑣú3CṹûᑣÊË1QḄᙳ┯öᭆ᳛஺VWᎷ:qᐭFGHüq"FGHᑖó#ý»,X2,X3ü஺ᢥ᯿ᨬᜧøᯠCṹûᑣ⌱᝞(/)=(")=X2E(ᑶ)=X3ᙳ┯ᭆ᳛PE=<

9711it761I=fl+f+l+41211

98ᨬ*┯ᭆ᳛+ṹ:ᑣ᝞:=XI?<*>=.R<ᑶ>=X3CD┯ᭆ᳛£=<

99(2)MNCṹḄṹ᳛R,ᎷXṹᭆ᳛ᑖ;«C——++—+——

100(3)ᵨᨬ*+ṹᑣ-¡¢ᦈ¤ᑡ10000,01100t00100+ᡂ¦§ṹk(4)Cṹfm`¨}ṹᐗḄ┯kr(1)CṹḄᨬ*dmin=3(2)CṹḄṹ᳛R=«¬W®ᱯ/ṹ°±n5(3)ᵨᨬ*+ṹ-10000+ᡂ1001001100+ᡂ1110000100+ᡂ11100.00111ᙳ(4)ᵫ³J„„„=3=2.l+l,CCṹfm`1}ṹᐗḄ┯஺[6.4]XYZ[Rᐗ\]⍝Ḅ`ab⌴ᭆ᳛p,┯b⌴ᭆ᳛p=11p«po·O¸஻ḄMºRᐗṹ(I=(a.ian…a”),ᐸ_a”D{0,1}(ṹᭆ᳛ᑖ)-¢ᦈḄRᐗ¤ᑡ@=(஻ÁÂ…ᔊ)-{0Ä}஺ÅÆᵨᨬ*+ṹᑣÇᙳ+ṹ┯ᭆ᳛Pr.Èᑮᨬ*-ÊËPf=lIÅÆ:᪀⌼Îᦪ/(x)=p,p*-ᨵ/2(x)=pxp\xInpIpApInp<0nCÑÎᦪÒÎᦪ-ᓽx஺,ÔD,D-ᨵp»p""’ᨬ*⌱Ḅ+ṹ:ᑣF(ত)=஺-ÇDr6D”ᡂÚ-ÛᯠÝᨵ

101PEePE2ᐸ_PEᨬ*+ṹÞᑮḄ`aᭆ᳛,ßP/ᑣpᐸà+ṹÞᑮḄ`aᭆ᳛,epij஺Cᢥ᯿£P„p'n}Dii,ᓽ

102áâãÞᑮäᵨᨬ*+ṹÞᑮḄ┯ᭆ᳛ᨬ*஺[6.5]³ᦣYZ[æ\]⍝-]⍝5▣IPPr11r|1IrI1mrill::Ipppr11rI1çÅƳC]⍝-ᨬ*+ṹᑣè³ᨬᜧéᯠ+ṹᑣ஺ÅÆx]⍝ê〈°±¤ᑡìᡂ••“->-¢ᦈ°±¤ᑡ@=<ᔊ1-b,?îP@|fi?=P<ïh,2•■■bin|ank…a,?=P3b\|aJd|an?•••P3bj.\a,.?Md''ᢥ᯿ᨬᜧéᯠ+ṹ:ᑣ-⌱<ᵯ>=<*,Ç>pτq*?rp>@k?ᡂÚ-ᓽLpஹᡠ-'®->MdMU''CᨵLPIMiâôõö-p=l[pு,Cᨵ£ø<ù*,@?ᡂÚ-ßúᓽᨬ*+ṹ:ᑣ஺12

1035▣P111IprI1.1IpPII;:I11•1IpIrI1P=f----I(11஺þ®)(1IP).D(ீ,®)>U(1I>(llp)[6,6]⍝ᐸᐭXḄ{0,1},rḄ{0,1},⍝

104"—II22IloilᨵḄ!"#⍝$(%ᭆ᳛)஺*+,-.ṹ,C:{(xi,%2,,)},780ᡈ1(z=1,2)ᡃ>⌱#᪵Aṹ1122ᐸṹB஻=4,E⌱F#᪵ḄGṹHᑣ1122(1)#᪵.ṹJ⍝Ḅ$᳛%KLMN(2)OPᙠ⌱ᵨḄGṹHᑣS+ᡠᨵṹUP£=0OWXᐭṹUYḄ▢[᳛00.401-10—11—ᳮ2^:/abc22A-00001/44000011/400000101/400000111/4000010001/400010101/400011001/400011101/4001000001/401001001/401010001/401011001/4011000001/411010001/411100001/411110001/4

105efg!"hiGṹ+jkᨵᐭlᐸ+m!"no,epᐸqᙳ┯tᭆ᳛PE=O஺[6.7]ὃ⇋ṹB4Ḅ{ᐗṹᐸṹU%=0000,}2=0011,IV,=1100,^=1111oᎷṹU〈ᐭ{ᐗ+⍝(ᐸᓫ┯tᭆ᳛pp<0.01),ṹUᐭ%ᭆ᳛Ḅᐸᭆ᳛1111P(%)=P(W?)=P(M)=P(M)=Zoo4AGṹHᑣqᙳ┯tᭆ᳛pᨬ஺EW:ᦈṹUU,ᑣᐳeᨵ16AḄṹUᑡ0,▢pDVj.Wi
Pᓃ|W=pᑡᡠᨵḄ᝞S⊤ᡠ£஺

106VIFᦈ¥Vᔆqooo-70cm-~~W-1-2.21.1-112©/3ᧅVrM°-pcvrl^n4PV1WnnnnnnnnUUUUeUUUU{nnnjnn2nn2nnnnUUU1KK•*KK§UUUUnPf724noinccccUU1U´pp,PP3PP?uuuu1-1CA4-1UUii2¶12᝞1PPUV111JL21”cinnnn?nnnnVIVUº2P1pp/'7,1,UUUU1JL2122nininnnnU1U1PPUUUUᳮ’0110^rPPpp—F--p-p0000A-L2”ni1inn?1111vl11½if/1pp1111J.a1_L211AUAUAUnn2AAAA1ppKK*uuuurr1-2.2innicccctuuiP/PPuuuu1Ãi1nUi1nU2Hn[PpnvnVcvicUx1«Z2Lpp"iniinn?1111tut1pp/1/1**A1PIlli11nn11nnttuu2”p1/ᶭ1tuuiiniInn,il,111111U1pp1111Z4½”1-12r1111n1111111U2"ÇLPPpp1iri1111pPPPPp1111

107[6.8]--AÉᦣËÌÍ⍝ᐸ⍝Î▣-1--Oo211C.--OIIL2211o--221oo-C2/TOOO(1)no⍝ÐÑC12᝞ÒᢥᨬᜧÕᯠGṹ×ᑣnGṹᘤÙGṹᘤÚḄqᙳ┯tᭆ᳛P(ᐭṹU%ᭆ᳛)஺E(3)ᨵËeÛᙠṹB2Ḅṹᓃ,)=0(Z=1,2,3,4,5),ᓽP஻=0,᝞ÛᙠḄÞßᩭ஺WX(1)áâã⍝ᐸj-ᦪåkæ-ᦪåḄçᣚjᑡᦪåkæᑡᦪåḄçᣚéêã⍝+⍝ᐸ⍝ÐÑX1122(2)Ꮇ⍝YḄᐭë{0,1,2,3,4},,-{ìíîṹ.p00ஹ11ஹ22ஹ33ஹ44ᐸṹ᳛R=ðJêñòeᨵ25Aeឋ,-ᨬᜧÕᯠGṹ᝞S⊤ᡠ£஺

108┯tᭆ᳛ITp=IooI2ṹB2Ḅíîṹᐸ$᳛log5ᓽ5ṹU஺C=logrI”,0,0,0=log5I1=1.322ôᱯ/ṹ=log5ôᱯ/ṹ஺

1091L111115144444J4(3)ö25B÷2Ḅᑡ᣸ᡂòᙽû᝞Sᡠ£:000102030400101112131410202122232420303132333430404142434440000102030400

110qᙳ┯tᭆ᳛0,7ᐙᑖᑭᵨGṹHᑣᎷ᝞⌱ÿ
ṹᑣᙠᐭᑡᑡṹ0011223344001/40001/400/44011/40000000200000ᙳ0300000ᙳ0400001/444101/4000000111/41/400000/111201/4000111300000ᙳ1400000ᙳ2000000ᙳ2101/4000112201/41/40011/2223001/400222400000ᙳ3000000ᙳ3100000ᙳ32001/4002233001/41/4022/33340001/40334000001/4444100000ᙳ4200000ᙳ430001/4033440001/41/433/44

111ᦈᑡṹḄᩩᭆ᳛Ḅ!"ᙠᡠ⌱Ḅṹ%&'ᓽ)᝞+
ṹ,⌱ᑣ-./&0Ḅ123Ḅ4ṹᙳ!"ᙠṹ%56-⌱7{00,12,24,31,43},-ABCᙳ┯Eᭆ᳛0o[6.9]BLMᐗO2஻+1,1RSTṹUVᵨᨬᜧZᯠṹ\ᑣ]ṹḄCᙳ┯Eᭆ᳛2«+1PE=஺pkp2n+llkk=n+\_pMᐗ`a⍝Ḅ┯Ec᳛defU“=5,7,9,11]AḄlZm஺BLnoMᐗO2஻+1,1RSTṹVᵨᨬᜧZᯠṹpᑣ]ᦈᑮḄṹᑡ!ᨵ22ᵪ6]-tuv11wxnw┯E56Cᙳ┯Eᭆ᳛nk=n+l2M+1PE=C2rt/t++llPn+1Pn+***+C22/ut++l1pIn+1—2rtl

112Pk/72n+lU0001020304L0II12131420212223R%313233344041424300]/41/41/41/011/41/41/q1/402L/4"Q1/41/403IB1/41/41/4041/41/41/4J/4101/41/41/41/4]]1/41/41/41A121/41/41/41/4௃31/41/41/41/4341/41/4]/41/4201/41/41/41/&211/41/4W1/4221/41/41/41/441/41/4V4]/4211/41/41/41/4Ll1/41/41/41/4311/41/41/41/4z:1/4V41/41/4331/41/41/41/4K1/41/41/41/4401/4]/41/41/4111/4lAi/a1/44/1/4i/a1/41/4431/41/41/41/411]/41/4”41/4

113U஻=2]PE=110B|U஻=3]}£=3.421017|U஻=4]PE=1.22101s|U”=5]P=4.43-10noot[6,10]Mᐗ(2n,l)STṹe
ᔠ〉Ḅṹpᑣd.ḄṹCᙳ┯Eᭆ᳛PEOn6⚪ᙠᐵᙠoo┯஻w]Ḅᜐᳮ2஺ᯠo┯Eonw]ᡃ-tuv1ᐸ┯Eo┯nw],!ᢣ•஺ᧁ"P"P"+

114¤¥¦§¨⚪[8.1]ᭆ᳛ᑖª(1/3,1/5,1/5,2/15,2/15)a«ḄMᐗ¬®ṹ஺¯°6ṹoᭆ᳛ᑖª(1/5,1/5,1/5,1/5,1/5)Ḅa«±)ᨬ²Mᐗṹ஺³MὅḄṹµᐰ·¸஺

115[8.2]Mᐗ¬®ṹ(00,01,10,11)º(0,10,110,111),-»¼᪵¬®ṹḄa«Ḅᡠᨵᭆ᳛ᑖª஺Ꮇ4a«¿ÀḄᭆ᳛ᑖÁ)pi,p2,p3,pa,Ꮇ,ᑣÄᨵ᝞ÅᩩᡂÇpi3P3+/74ÊPl+P2+P3+஻4=1,ᓽP3+P4£,56⌕᪀⌼&λṹÄ⌕ÏÐpi8pi+pa131஺+Ñ£-/718/73+P4p23P3+pa»ṹ(0,10/10,111)Ḅṹ᪛᝞Å'ᡠÔ:

116᝞+ᢥ&ÎÖ×ØÙ»ṹÄ⌕ÏÐ"3Û,p,+pa9஺56µᡂ&λṹḄᭆ᳛ᑖªn1ßு3pi3Plp.3+P4cpi[8.3]a«¿ÀáIS1I51521ââ(1)"(S)ºa«ᑍåæ|(2)ṹ¿ÀX={0è},»SḄéêṹdSḄéêṹḄCᙳṹëL|(3)ìa«ḄNíîïð᡽òa«S.v»ᡂéêṹôN=2,3,4,]ḄCᙳṹëb|N(4)ef&ÎN=l,2,3,44ṹḄ»ṹᦔ᳛ºṹᑍåæ஺:(1)a«ø

117H(S)=I

11856¼a«ᑍåæ©=[[᝛=0.531logrO2RᐸØÙéêṹ»ṹMa«¿À
»ṹ0,
»ṹ1,56Cᙳṹë1ṹ¿À/a«¿À|Cᙳṹën_L2=0.81+0.18+0.27+0.03=1.29;=0.645ṹ/᡽᡽!ISSSiSISIS25152slS1S2S2S2sss2sls25252slSiS2sl10.7290.0810.081O.I2O.90.081O.I2O.90.k0.9.h|JOHuffman.ṹṹ/᝞1:

119᡽Ḅ4ᙳṹ6!:Li=0.729+0.081*9+0.009*15+0.005=1.598-=0.532667ṹ/N7᡽ᶍ9:N;᪷=✏?@ABᳮ4ᙳṹ6!DEF=0.469ṹ/NlogrG5.ṹᦔ᳛!D/="KDUmN10gfLMᨵO᡽;.ṹᦔ᳛!D/=P=0.469A᡽;.ṹᦔ᳛!D/=᝛=0.727LR᡽;.ṹᦔ᳛!D/=P=0.880476:N;.ṹᦔ᳛SᔣUkLMVW⚪YZ[\]U^6_`ṹ᡽ḄᦪO◤cᜧ;e

120[fgᑮiᦔḄjᜫl.ṹmAnEo6ṹᨵcᜧḄOp஺LN

121[8.4]!|PG5r|ṹ!X={0,1,2},s᪀⌼AvᐗḄ_`ṹ஺xDᨵ8y!zᨵᦔᑭᵨ}ṹ◤᡽~1yᭆ᳛!0Ḅᐸ9=2*3+3ᡂ஺.ṹ᝞1:00.410.410.4000.20.2200.2020.10.201200.10.112210.050.12220.0500100.0510110.0520120[8.5]ᕒ᝱ᨵ7v[ḄDᨒஹஹ஺yoᭆ᳛Ḅ〈yᨬ¢ᡠ◤ḄRᐗᾭ¥ᦪ¦¢§¨7y88fx1D¢§᝞©.ṹ§4

122ªᙠM¬1ᡠ◤ḄRᐗᾭ¥ᦪ¦:III0.40.20.10.10.050.050.050.05J]®Ḅᭆ᳛ᑖ°!ஹஹ

1234ᙳy±²Ḅ³!2´ᱯLM〈yᨬ¢◤⌕ḄRᐗᾭ¥ᦪ!2஺᝞·7y¸oᭆ᳛ᑖ¹ºᵨ_`ṹ.ṹ[ᡠ◤⌕ḄRᐗᾭ¥ᦪᨬ¢.ṹ᝞1D4ᙳṹ6!DL=4pgr/,=1.75Rᐗṹ/ᓽᙠM¬1ᡠ◤ḄRᐗᾭ¥ᦪ!1.75y஺[8.6]AᨵNy¼½yoᭆ᳛]®mᵨᨬ¾¿ÀÁṹRᐗ.ṹª:N=2,N=2,+lGzÂ᦮ᦪr;yṹ/Ḅ6ÄoU¦¢§4ᙳṹ6¦¢§xD1
:N=29;y.ṹᡠḄṹ/!o6ṹᐸṹ6!i,4ᙳṹ6L=i9G2
:N=2,+l;.ṹ;ÅÆᒕÈAyLMᡃÊ[fᐜÌÍyÎÏÎÏÐḄyᦪាÒ!2,yÓm2,y.ṹ;o6Ḅᐸṹ6!i,ᐸÕᒹ×!2Ø1yp

124;Ù᜜ÍyḄṹ6!i+1,LMḄ4ᙳṹ6!

125,/(2.I1)+2(/+1)ফ+i+22L='''2+1[8.7]àIsS25,1/11SM1p\P2•••PM11p,w|J,wṹ஺ᐸṹ/WMᐹᨵâpḄ6ĽW.M!IW”çᨵᨬÐAèṹOp(ᑖ°!10)஺xDëì᯿îW264⚓ᨬ¾ṹyឋñḄòóMᜐᶍ஺[8.8]àṹCᙳᒴᭆ᳛ᑖ¹P=(1/஻//஻…Ø/஻)ḄRᐗ¿ÀÁṹ஺¼àṹCÕᔜṹ/Ḅṹ6!/.,uvn=a2",Ó16a32஺(1)òóUMoᭆ᳛Ḅᡠᨵᓽ;ṹÕṹCḄÅṹ6T=஺C2ᐸBṹ3ᨵLC2>L,D<ᙳ(ṹLc=,L(2=EFI73T2

126J2KL஺=17ᡠᨵṹḄṹMNᙳ"ki+2+12+15:I)STUVp,=l!pie/?2e•••ePMO\#$]^_`3aᙠb᪵Ḅ&ᐗᨬd

127L஺=27ᡠᨵṹḄṹMNᙳ/-᝕+1DL1V஺V27_`ghᦪi^2*klmḄno᦮ᦪqrᙠṹ᪛tr3uvkḄ⁚xtyzᑖ|}v&+1ḄṹJJ3K⚪;ᡠḄṹ⌕L\\=k,⌕L=k+loṹkḄ⁚xᦪx,ᑣṹk+1Ḅ⁚xḄᑖ|ᦪ3J24.0.2,Dᐸ┠ᦪ%x+J2Jl.rK-2=2i»ili=a2Jᨵ=X2IA4-2^Ix•2•2IHIIkkIk&1J3KᙠJ2K⚪;$ᜐᶍ஺J4K᪷J2K⚪;Ḅᑖ᪆E0=k+1,ᨵu-\-v=a2kv=2k+iI2uFu=22+iIa2kv=2a2kI2A+I=J஻1lK2&+i+ṹḄ<ᙳṹL%2GK+ᓄ]%-[h+2aI2]

128=k+2\~a=x2

129[8,9]¤ᨵ3¥¦ᦣ¨ᓄḄ©ª©ªḄᮞv¨ᓄᑖᡂ8®¯⊤஺⊤;ᦪMrª±tḄᮞv஺²ᨵ3³´³µ&ᐗ_⍝ᓫi7mJ·Kᑁ¹º100&ᐗgh஺J1K¤»©ª¼½¾Ḅ_⍝¹º¿ὃ⇋©ªḄÂÃÄÅᱯឋSÇᵨ&ᐗNṹÉ◤⌕Ë7mÌ͹Îb¥©ªÏJ2KÐὃ⇋©ªḄÄÅᱯឋJ¿ὃ⇋©ªḄª±lmḄÑÒឋKÓ©ªḄ_`Ô”JSK,S]ᮞvÖ×()*ᨬd&ᐗ+ṹÉ<ᙳت±◤ᵨËÙ&ᐗṹghᩭ⊤ÛÏb7◤ËÙ7mÌ͹〈Îb¥©ªÏJ3KÝᳮßtà⌕$b¥©ªáEâãD<ᙳت±ᡠ◤Ḅ&ᐗṹghᦪE^H3Säᱯ஺%J1KÇᵨ&ᐗNṹ¿ὃ⇋_`ghḄÄÅᱯឋ<ᙳØᮞv◤⌕3i&Öᑴ⊤Ûᙠ10*10Ḅ©ªtᐳ◤300i&Öᑴ⊤ÛØ·¹º100iÅçᐳ◤3·è¹º஺J2KÄÅ©ª;ᔜᮞvḄz¤êᦪ%12345678401710107655

130᝞íὃ⇋_`ghḄÄÅᱯឋ]tîᮞvÖ×+ṹ᝞¯©ᡠÛ஺1111111111111111111111111111111111111111222222222222222223333333333444444444455555556666667777788888

131F᝞¯ṹ:12345678401710107655010010101011110011011110111113444444<ᙳṹ%L=0.4+0.51+0.43*4=2.63ᙠ10*10Ḅ©ªtᐳ◤263i&Öᑴ⊤ÛØ·¹º100iÅçᐳ◤2.63·è¹ºÎ஺(3)ᙠÅç(2)⚪7Sïὃ⇋ª±ᮞvlmḄÑÒᐵñò᝞ᮞv1óÍôᮞv1!2,SïᨵᐸBᮞvõ஺b᪵FᑮḄ_`ÔH

1320.1,0.1,0.1஺./ᡂ123ᐗ456ṹ789Ḅᙳṹ6:;<ᐹᨵ>;Ḅ10010101W111001J/J7110111101111

133ṹ6Ḅ?@ABCᙳṹ6D?@EFG2ṹHIᵨK஺LMNO3ᐗ/ṹ◤P⊡ᭆ᳛(0Ḅ!"12/ṹ?R᝞TᡠU஺V1V2ᙳṹ6(ML=0.2+0.3+0.3+0.6+0.6=2/ṹ1Ḅṹ?@(M&=£[(/,1L)]=0.2+0.1+0.1=0.42W=£[(/.IL/]=0\ᯠ12/ṹḄᙳṹ6:;<ᵫ_/ṹ2Ḅṹ?@`abc/ṹ2HIᵨK஺[8.11]dᨵ1!"xDy᝞T:1x1

134P(x)lIXX2X3X4X5X6Xi10.20.190.180.170.150.10.01J

135|pfy|=10.490.140.140.070.070.040.020.020.01IIyேெyiWytgy3,yi**1jjf1kᑖmᵨnopṹ/ᡂᐗq6rstṹABCᐸ/ṹᦔ᳛v
2ᑖmᵨ✏x/ṹR/ᡂᐗq6rstṹABC/ṹᦔ᳛vf3ᑖmᵨyz/ṹ?R/ᡂᐗq6rstṹABC/ṹᦔ᳛;
4k|xஹy12>;!"ᩭ`32/ṹ?RḄ஺LM!":!"(:”fXk=[

136/==0.95907ᐸNOyz/ṹ᝞TᡠUM000.200100.190010110.181100.1701100.15]011100.11101111110.01ᙳṹ6(:£=0.4+0.37*3+0.34+0.45+0.44=2.74ṹ/!"/ṹᦔ᳛(M/==0.95207ᐸNO✏x/ṹ᝞TᡠU஺ᐸᙳṹ6(ML=0.89*3+0.4+0.07=3.14ṹ/!"/ṹᦔ᳛(M/==0.83079!"M!"(:

137“(y)=[

138ᐸNOᐗnop/ṹ᝞TᡠU஺ᙳṹ6(ML=0.49+0,28*3+0.18*4+0,02*5+0.03*6=2.33ṹ/!"/ṹᦔ᳛(M/==0.99294LJᐸNOyz/ṹ᝞TᡠU஺00.4901000.14o0°11010.1411000.07000111010.07111100.04I0111100.02,01111100.02110111111110.01ᙳṹ6(:L=0.49+0,28*3+0.18*4+0.02*5+0.03*6=2.33ṹ/!"

139/ṹᦔ᳛(:

140----\10.99294ᭆ᳛ṹ6ᭆ᳛᜛ᡡNᑴaᦪṹO✏7᝞Tᡠ-200.0000.1430.490.0111110101110110.1430.630.1010000101001010.0740.770.11000101000111000.0740.840.11010111000011010.0450.910.111010001111111010.0260.950.1111001100111111000.0260.970.1111100001011111100.0170.990.1111110101111111110ᙳṹ6(ML=0.49*2+0.28*3+0.14*4+0.04*5+0.04*6+0.01*7=2.89/ṹᦔ᳛(M/==0.80054|/ṹsnop/ṹḄᙳṹ6ᨬ¡/ṹᦔ᳛ᨬ¢✏x/ṹḄᙳṹ6ᨬ6ᐸ/ṹᦔ᳛ᨬ£yz/ṹ¤஺[8.12]!"¥A-{1,2,...,q},ᐸᭆ᳛ᑖ(p\,p2o¦ᵨT?R!"NO/ṹ஺✌ᐜ©ᭆ᳛ᑖᢥᜧa¬᣸ᑡp.epe-.eA,°±ᑖ²ᦪ-illk=\³´µ1¶☄¸¹º»ᐹ¼IḄṹ½¾F.ḄNᑴᦪḄaᦪ¿,I11IpiI(1)ÀF᪵/ÂḄṹ½ᓽÄṹ;

141(2)ÀFMH(S)5LãäḄáâᐸNᑴaᦪḄèéêᑖ½>;Ḅᡠ᪵ÂᑮḄṹ°ìíq6ṹḄèéᩩïbc½ᓽÄṹ஺

142P'8+/,<1,lobcgᨵòL=Ilog-I,Âlog—f2k᪷æh=Ilog—I,Âlog

143p,log8P'ItS?6ù<஻>S?+1ṹᭆ᳛ṹᑖNᑴaᦪ2\Vd-1÷øWùûü>ý>þvÿ
Art-FT“4g.5,0“U.123Jᔩ1141᝞1100.2520.50.11100.12530.750.111110.12530.8750.1114ṹḄṹᐰ"#ᓽ%&'᪀⌼ᡂ+Ḅ,#ṹᐸ./0ᐸṹា23log1,Ḅᐜ7ᭆ᳛ា232Ḅ:;<ᑖP
&[8.14]=>ᐗ0,1ᐸp0=,pi=᪀ᡂ+✏AB"CᳮE▲ᡂGḄᩩI/JᯠLM᪀⌼N,#ṹ஺PQRᐸSTUVṹWXUOOYᑡḄ[ᙳṹ11111110111110]^_ᑡḄ`aᭆbc'។9122122I0ᙠṹghRiᑡᬰklmJ12*log7+2*3I=[8.3111=9IillI81ps|||ṹᙠṹ᪛oḄpRqr᝞Esᡠu:

144/LwṹYᑡḄᑖxᦪ3:F(S)=1IP(llllllll)IF(ll11111011111)=11f11fl.29ீ88)8=0.631213929ᑖxᦪ3>Sᑴᦪw0.101000011001,ᦪ9qWSTSqᜐᳮwoYᑡḄṹ3101000100c[ᙳṹ301=,=0.6429ṹ/14ṹᦔ᳛3:H(S)

145L

146[8.15]Rᐭᦪ000010110011100001001101111ᑖᵨLZ-77U¡ஹLZ-78U¡LZWU¡ஹK-YU¡STṹWXUᔜ¤<¡Ḅ¥¦᳛஺]^§ᵨLZ-77ṹᡠwḄṹYᑡ3^(0,0,0)(1,3,1)(0,0,1)(2,2,1)(6,3,1)(5,3,0)(13,3,0)(9,3,1)(14,3,eoD¬ᵨLZ-78ii1000,100,11,0111,11ᐺ®¯ᩩ°`〈YᑡJ^³Ḅ4¶¸_¹´77rl-F²´'Jµ”º4110(0,0)200(1,0)301(1,1)4011(3,1)5001(2,1)61(0,1)710(7,0)8000(2,0)9100(7,0)1011(6,1)110111(4,1)(10,eof)

147§ᵨLZWṹ»¼᝞E:K-YU¡^½D0=0,Dl=l,ᐜ¾ᐭ4¿0000,ÀpÁ/ᨚgṹD2D2ᐸÃD2=DODOÄÅᐭÆD2D2DiDoDiDo,NÇÈÉÊ˽DIDO=D3=1O,ᑣYᑡ3^D2D2D3D3,ÄÅᐭwD2D2DsDaDoD1D1D1D2D2½D4=D2D2=0000,oYᑡ3^D4D3D3D0D1DτD1D4DτDoDoD1½D5=DODI,oYᑡ3^D4D3D3D5D1D1D4D1D0D5D1½D6=DDIoYᑡ3^5D4D3D3D6D1D4DτDoDbDoD1D1D1D1½D7=DlD!=lLoYᑡ3D4D3D3D6DτD4D1DoDoDoDvD7ᐸÃDo=O,Di=l,D2=00,D3=10,D4=0000,DS=01,D6=011,D7=ll

148oYᑡMÍᐺ`〈ÆÎᦈ<ᓽL஺10Ð&ᐺ21300140003501161027011581006901117101000811001312100181311214101615111131113,eof