3.15.yingyao.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300
TeXDict begin @letter
%%EndSetup
%%Page: 1 1
bop 812 307 a Fl(Solution)17 b(to)f(3.15)866 357 y Fk(Yingw)o(ei)d(Y)m(ao)262
407 y(3.15)f(Giv)o(en)h Fj(a)i(priori)f Fk(probabilities)f
Fi(\031)885 413 y Fh(0)903 407 y Fi(;)7 b(\031)946 413 y Fh(1)964
407 y Fk(,)13 b(the)i(optim)o(um)10 b(detector)16 b(claims)1525
396 y(^)1526 407 y Fi(b)11 b Fk(=)h(1)i(if)701 482 y Fi(\031)725
488 y Fh(1)744 482 y Fi(f)t Fk(\()p Fi(y)q Fg(j)p Fi(b)e Fk(=)g(1\))g
Fg(\025)f Fi(\031)1007 488 y Fh(0)1026 482 y Fi(f)t Fk(\()p
Fi(y)q Fg(j)p Fi(b)h Fk(=)g Fg(\000)p Fk(1\))p Fi(:)262 557
y Fk(F)m(or)h(conciseness,)j(denote)566 631 y Fi(f)590 614
y Ff(\000)619 631 y Fk(\()p Fi(y)q Fg(j)p Fi(b)c Fk(=)g Fg(\006)p
Fk(1\))g(=)f Fi(f)t Fk(\()p Fg(f)p Fi(y)q Fk(\()p Fi(t)p Fk(\))p
Fi(;)c(t)13 b Fg(2)e Fk([0)p Fi(;)c(T)e(=)p Fk(2])p Fg(gj)p
Fi(b)k Fk(=)j Fg(\006)p Fk(1\))562 706 y Fi(f)586 689 y Fh(+)614
706 y Fk(\()p Fi(y)q Fg(j)p Fi(b)g Fk(=)g Fg(\006)p Fk(1\))g(=)g
Fi(f)t Fk(\()p Fg(f)p Fi(y)q Fk(\()p Fi(t)p Fk(\))p Fi(;)7
b(t)12 b Fg(2)g Fk([)p Fi(T)5 b(=)p Fk(2)p Fi(;)i(T)f Fk(])p
Fg(gj)p Fi(b)i Fk(=)k Fg(\006)p Fk(1\))262 771 y(Then)565 847
y Fi(f)589 830 y Ff(\000)618 847 y Fk(\()p Fi(y)q Fg(j)p Fi(b)g
Fk(=)g(1\))f(=)h Fi(exp)p Fk(\()p Fg(\000)972 819 y Fk(1)p
950 837 65 2 v 950 875 a(2)p Fi(\033)996 863 y Fh(2)1027 790
y Fe(Z)1073 789 y Fd(T)p 1073 794 21 2 v 1076 811 a Fc(2)1050
885 y Fh(0)1101 847 y Fk([)p Fi(y)q Fk(\()p Fi(t)p Fk(\))e
Fg(\000)1254 819 y Fi(A)p 1238 837 65 2 v 1238 846 a Fg(p)p
1272 846 31 2 v 1272 881 a Fi(T)1307 847 y Fk(])1319 830 y
Fh(2)1337 847 y Fi(dt)p Fk(\))549 976 y Fi(f)573 959 y Ff(\000)602
976 y Fk(\()p Fi(y)q Fg(j)p Fi(b)i Fk(=)g Fg(\000)p Fk(1\))f(=)h
Fi(exp)p Fk(\()p Fg(\000)988 948 y Fk(1)p 966 967 65 2 v 966
1005 a(2)p Fi(\033)1012 993 y Fh(2)1043 920 y Fe(Z)1089 919
y Fd(T)p 1089 924 21 2 v 1092 940 a Fc(2)1066 1014 y Fh(0)1117
976 y Fk([)p Fi(y)q Fk(\()p Fi(t)p Fk(\))e(+)1270 948 y Fi(A)p
1254 967 65 2 v 1254 975 a Fg(p)p 1288 975 31 2 v 1288 1010
a Fi(T)1323 976 y Fk(])1335 959 y Fh(2)1353 976 y Fi(dt)p Fk(\))569
1100 y Fi(f)593 1083 y Fh(+)621 1100 y Fk(\()p Fi(y)q Fg(j)p
Fi(b)i Fk(=)g(1\))f(=)h Fi(exp)p Fk(\()p Fg(\000)975 1072 y
Fk(1)p 953 1091 65 2 v 953 1129 a(2)p Fi(\033)999 1117 y Fh(2)1030
1044 y Fe(Z)1071 1054 y Fb(T)1058 1127 y Fd(T)p 1058 1132 21
2 v 1061 1148 a Fc(2)1098 1100 y Fk([)p Fi(y)q Fk(\()p Fi(t)p
Fk(\))d Fg(\000)1251 1072 y Fi(A)p 1234 1091 65 2 v 1234 1099
a Fg(p)p 1269 1099 31 2 v 35 x Fi(T)1304 1100 y Fk(])1316 1083
y Fh(2)1334 1100 y Fi(dt)p Fk(\))553 1233 y Fi(f)577 1216 y
Fh(+)605 1233 y Fk(\()p Fi(y)q Fg(j)p Fi(b)j Fk(=)g Fg(\000)p
Fk(1\))f(=)h Fi(exp)p Fk(\()p Fg(\000)991 1205 y Fk(1)p 969
1224 65 2 v 969 1262 a(2)p Fi(\033)1015 1250 y Fh(2)1046 1177
y Fe(Z)1088 1187 y Fb(T)1074 1260 y Fd(T)p 1074 1265 21 2 v
1077 1281 a Fc(2)1114 1233 y Fk([)p Fi(y)q Fk(\()p Fi(t)p Fk(\))e(+)1267
1205 y Fi(A)p 1250 1224 65 2 v 1250 1232 a Fg(p)p 1285 1232
31 2 v 35 x Fi(T)1320 1233 y Fk(])1332 1216 y Fh(2)1350 1233
y Fi(dt)p Fk(\))262 1329 y(The)k(\\a)f(priori")g(probabilities)i(~)-23
b Fi(\031)798 1335 y Fh(0)830 1329 y Fk(and)16 b(~)-23 b Fi(\031)935
1335 y Fh(1)967 1329 y Fk(are)264 1428 y(~)g Fi(\031)286 1434
y Fh(1)315 1428 y Fk(=)607 1399 y Fi(f)631 1384 y Ff(\000)660
1399 y Fk(\()p Fi(y)q Fg(j)p Fi(b)12 b Fk(=)g(1\))p Fi(P)6
b Fk(\()p Fi(b)11 b Fk(=)g(1\))p 364 1418 858 2 v 364 1456
a Fi(f)388 1444 y Ff(\000)417 1456 y Fk(\()p Fi(y)q Fg(j)p
Fi(b)h Fk(=)g(1\))p Fi(P)6 b Fk(\()p Fi(b)k Fk(=)i(1\))d(+)h
Fi(f)810 1444 y Ff(\000)839 1456 y Fk(\()p Fi(y)q Fg(j)p Fi(b)i
Fk(=)f Fg(\000)p Fk(1\))p Fi(P)6 b Fk(\()p Fi(b)11 b Fk(=)h
Fg(\000)p Fk(1\))1238 1428 y(=)1434 1399 y Fi(f)1458 1384 y
Ff(\000)1487 1399 y Fk(\()p Fi(y)q Fg(j)p Fi(b)g Fk(=)g(1\))p
1287 1418 508 2 v 1287 1456 a Fi(f)1311 1444 y Ff(\000)1340
1456 y Fk(\()p Fi(y)q Fg(j)p Fi(b)f Fk(=)h(1\))d(+)h Fi(f)1574
1444 y Ff(\000)1603 1456 y Fk(\()p Fi(y)q Fg(j)p Fi(b)i Fk(=)f
Fg(\000)p Fk(1\))672 1557 y(~)-23 b Fi(\031)694 1563 y Fh(0)724
1557 y Fk(=)904 1529 y Fi(f)928 1514 y Ff(\000)957 1529 y Fk(\()p
Fi(y)q Fg(j)p Fi(b)12 b Fk(=)g Fg(\000)p Fk(1\))p 773 1547
V 773 1585 a Fi(f)797 1573 y Ff(\000)825 1585 y Fk(\()p Fi(y)q
Fg(j)p Fi(b)g Fk(=)g(1\))d(+)h Fi(f)1060 1573 y Ff(\000)1088
1585 y Fk(\()p Fi(y)q Fg(j)p Fi(b)i Fk(=)g Fg(\000)p Fk(1\))262
1644 y(So)h(in)h(this)g(t)o(w)o(o-stage)f(detector,)i(the)g(decision)f
(region)g(for)f(the)i(h)o(yp)q(othesis)f Fi(b)d Fk(=)h(1)i(is)262
1743 y Fg(f)p Fi(y)q Fg(j)r Fk(~)-23 b Fi(\031)340 1749 y Fh(1)358
1743 y Fi(f)382 1728 y Fh(+)410 1743 y Fk(\()p Fi(y)q Fg(j)p
Fi(b)12 b Fk(=)g(1\))f Fg(\025)j Fk(~)-23 b Fi(\031)649 1749
y Fh(0)667 1743 y Fi(f)691 1728 y Fh(+)720 1743 y Fk(\()p Fi(y)q
Fg(j)p Fi(b)12 b Fk(=)g Fg(\000)p Fk(1\))p Fg(g)262 1804 y
Fk(=)f Fg(f)p Fi(y)q Fg(j)467 1784 y Fb(f)486 1772 y Fa(\000)511
1784 y Fh(\()p Fb(y)q Ff(j)p Fb(b)p Fh(=1\))p 364 1795 361
2 v 364 1819 a Fb(f)383 1810 y Fa(\000)408 1819 y Fh(\()p Fb(y)q
Ff(j)p Fb(b)p Fh(=1\)+)p Fb(f)563 1810 y Fa(\000)588 1819 y
Fh(\()p Fb(y)q Ff(j)p Fb(b)p Fh(=)p Ff(\000)p Fh(1\))729 1804
y Fi(f)753 1789 y Fh(+)782 1804 y Fk(\()p Fi(y)q Fg(j)p Fi(b)h
Fk(=)g(1\))f Fg(\025)1092 1784 y Fb(f)1111 1772 y Fa(\000)1136
1784 y Fh(\()p Fb(y)q Ff(j)p Fb(b)p Fh(=)p Ff(\000)p Fh(1\))p
1002 1795 V 1002 1819 a Fb(f)1021 1810 y Fa(\000)1046 1819
y Fh(\()p Fb(y)q Ff(j)p Fb(b)p Fh(=1\)+)p Fb(f)1201 1810 y
Fa(\000)1226 1819 y Fh(\()p Fb(y)q Ff(j)p Fb(b)p Fh(=)p Ff(\000)p
Fh(1\))1367 1804 y Fi(f)1391 1789 y Fh(+)1419 1804 y Fk(\()p
Fi(y)q Fg(j)p Fi(b)h Fk(=)g Fg(\000)p Fk(1\))p Fg(g)262 1863
y Fk(=)f Fg(f)p Fi(y)q Fg(j)p Fi(f)383 1848 y Ff(\000)412 1863
y Fk(\()p Fi(y)q Fg(j)p Fi(b)h Fk(=)g(1\))p Fi(f)596 1848 y
Fh(+)624 1863 y Fk(\()p Fi(y)q Fg(j)p Fi(b)g Fk(=)g(1\))f Fg(\025)h
Fi(f)863 1848 y Ff(\000)892 1863 y Fk(\()p Fi(y)q Fg(j)p Fi(b)g
Fk(=)g Fg(\000)p Fk(1\))p Fi(f)1108 1848 y Fh(+)1136 1863 y
Fk(\()p Fi(y)q Fg(j)p Fi(b)g Fk(=)g Fg(\000)p Fk(1\))p Fg(g)262
1963 y Fk(Substituting)h(the)i(expressions)h(of)d Fi(f)859
1948 y Ff(\000)888 1963 y Fk(\()p Fi(y)q Fg(j)p Fi(b)f Fk(=)g
Fg(\006)p Fk(1\))i(and)g Fi(f)1199 1948 y Fh(+)1228 1963 y
Fk(\()p Fi(y)q Fg(j)p Fi(b)e Fk(=)g Fg(\006)p Fk(1\))i(in)o(to)f(the)i(ab)q
(o)o(v)o(e)262 2012 y(equation,)e(w)o(e)h(can)g(get)g(that)g(the)g(decision)g
(region)g(is)808 2116 y Fg(f)p Fi(y)q Fg(j)869 2059 y Fe(Z)911
2070 y Fb(T)893 2154 y Fh(0)944 2116 y Fi(y)q Fk(\()p Fi(t)p
Fk(\))p Fi(dt)e Fg(\025)g Fk(0)p Fg(g)262 2212 y Fk(F)m(rom)g(here)j(it)e(is)
h(easy)g(to)g(sho)o(w)g(that)743 2305 y Fi(P)6 b Fk(\()791
2294 y(^)792 2305 y Fi(b)11 b Fk(=)h(1)p Fg(j)p Fi(b)e Fk(=)i
Fg(\000)p Fk(1\))g(=)g Fi(Q)p Fk(\()1149 2277 y Fi(A)p 1149
2296 32 2 v 1152 2334 a(\033)1185 2305 y Fk(\))p Fi(;)262 2399
y Fk(b)o(y)h(symmetry)f(w)o(e)i(ha)o(v)o(e)g(the)h(error)f(probabilit)o(y)f
(is)g Fi(Q)p Fk(\()1151 2383 y Fb(A)p 1151 2390 25 2 v 1153
2414 a(\033)1181 2399 y Fk(\).)967 2574 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF