.b w2HHi`+FBM;@6`K2rQ`F mb #b+?MBii kX9 HB272`i /B2 ;`mM/H2;2M/2M H;Q`Bi?K2M mM/ J2i?Q/2M- mK w2HH2M BM 2BM2` ;2;2#2M2M "BH/b2`B2 xm 2`F2MM2M mM/ Ƀ#2` /B2 w2Bi xm p2`7QH;2MX Lm` bQHM;2 /B2 "BH/b2;K2MiB2`mM; Uw2HH/2i2FiBQMV mM/ /B2 wmr2BbmM; /2`
w2HH2M xrBb+?2M /2M "BH/2`M Uw2HHi`+FBM;V 72?H2`7`2B 7mMFiBQMB2`2M- FMM 2BM2 pQHHbi M@
/B;2 :2M2HQ;B2 /2` #2Q#+?i2i2M w2HH2M 2ti`?B2`i r2`/2MX
AM 2BM2` mbr2`imM; pQM 2+?i2M "BH/b2`B2M Bbi 2b HH2`/BM;b MB+?i Kƺ;HB+?- 2BM2 72?@
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wmr2BbmM;2M 2Mi?Hi2MX lK /B2 mbrB`FmM; /B2b2` 62?H2` #xmb+? ix2M- rB`/ 2BM2 bvb@
i2KiBb+?2 MHvb2 /2` p2`b+?B2/2M2M 62?H2`[m2HH2M /m`+?;27Ƀ?`iX Mb+?HB2Ľ2M/ rB`/
/B2 62?H2`7Q`iT~MxmM; BM /2` ;2;2#2M2M "BM `#mK@ai`mFim` mMi2`bm+?i mM/ 2b rB`/
;2x2B;i- r2H+?2 mbrB`FmM; /B2b2 62?H2` m7 /B2 _2FQMbi`mFiBQM /2` pQHHbi M/B;2M :2@
M2HQ;B2M ?#2MX
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HB/B2`iX JBi >BH72 /B2b2` S`Qx2bb2 Bbi 2b Kƺ;HB+?- /B2 2ti`?B2`i2M w2HHT7/2 /2` h`+FBM;@
H;Q`Bi?K2M bvbi2KiBb+? m7 62?H2` xm mMi2`bm+?2M mM/ /B2 72?H2`?7i2M S7/2 mb 2BM2` r2Bi2`2M mbr2`imM; mbxmb+?HB2Ľ2MX
m7#m2M/ m7 /B2b2K JQ/2HH bBM/ xr2B FQMbBbi2Mi2- pHB/B2`i2_272`2Mx/i2Mb ix2 2MibiM/2M- /B2 bQrQ?H FQ``B;B2`i2 w2HHKbF2M Hb m+? FQ``B;B2`i2 :2M2HQ;B2M 2Mi?H@
i2M- /X?X D2/2 w2HH2 Bbi /2K `B+?iB;2M aiKK#mK xm;2Q`/M2iX .B2b2 .i2Mb ix2 M2?K2M BM /2M 7QH;2M/2M xr2B ETBi2HM 2BM2 x2Mi`H2 _QHH2 2BM mM/ r2`/2M p2`r2M/2i- mK /B2 w2HHi`+FBM;@H;Q`Bi?K2M mb #b+?MBii kX9 xm 2pHmB2`2M mM/ xm pHB/B2`2MX
.b pQ`;2bi2HHi2 pHB/B2`i2 w2HHi`+FBM; Bbi BM /2K w2HHi`+FBM;@6`K2rQ`F mb #@
b+?MBii kX9 BMi2;`B2`i mM/ BM /2` `#2Bi pQM _TQTQ`if"2+F2` 2i HX (3) p2`ƺz2MiHB+?iX .B2 pQHHbi M/B;2M _272`2Mx/i2M rm`/2M mMi2` /B2 *`2iBp2 *QKKQMb@GBx2Mx ;2@
bi2HHi- /X?X /B2 .i2Mb ix2 bBM/ 7Ƀ` D2/2`KMM 7`2B xm; M;HB+? mM/ FƺMM2M Hb "bBb 7Ƀ`
r2Bi2`2- p2`;H2B+?2M/2 mbr2`imM;2M mM/ 1pHmiBQM2M ;2Mmixi r2`/2MX
jXRX 62?H2`MHvb2 mM/ oHB/B2`mM; pQM w2HHi`+FBM;@.i2M
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jN
ETBi2H jX oHB/B2`i2b w2HHi`+FBM;
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i2Mbix ;2MmixiX
62?H2`7Q`iT~MxmM; BM x2HHmH `2M :2M2HQ;B2M
lK /B2 mbrB`FmM; /2` 62?H2`7Q`iT~MxmM; xm p2`Mb+?mHB+?2M- rB`/ xmM +?bi /B2 62?H2`M7 HHB;F2Bi BM /2M ;2;2#2M2M aiKK# mK2M #2i`+?i2iX .B2 MiɃ`HB@
+?2 "BM `#mKbi`mFim` #2rB`Fi- /bb #2`2Bib 2BM 2BMx2HM2` .2i2FiBQMb72?H2` 2BM2
;`QĽ2 mbrB`FmM; m7 /B2 _2FQMbi`mFiBQM /2` x2HHmH `2M :2M2HQ;B2M ?#2M FMM, Lm` r2MM pQM 2BM2` #2i`+?i2i2M w2HH2 HH2 L+?7QH;2` BM HH2M 7QH;2M/2M "BH/2`M FQ``2Fi 2`FMMi mM/ xm;2Q`/M2i r2`/2M- Bbi 2b Kƺ;HB+?- HH2 o2`rM/i2M- /X?X /B2
;2bKi2 w2HH7KBHB2- xm }M/2MX AK 6QH;2M/2M r2`/2M xr2B q?`b+?2BMHB+?F2Bi2M M;2;2#2M- /B2 #? M;B; pQM /2` :2MmB;F2Bi /2` w2HH/2i2FiBQM r bBM/,
RX .B2 q?`b+?2BMHB+?F2Bi- KBi r2H+?2` /2` S7/ 2BM2` w2HH2 Ƀ#2` 9y "BH/2`
`2FQMbi`mB2`i rB`/- 2`;B#i bB+? xm ppf ad(pi) =r40X
kX JBi ppf ad FMM MmM /B2 q?`b+?2BMHB+?F2Bi pgen M;2;2#2M r2`/2M- KBi /2` 2BM2 :2M2HQ;B2 2BM2` w2HH7KBHB2 2ti`?B2`i rB`/X 1BM aiKK#mK KBi n= 3 :2M2`iBQM2M 2Mi? Hi2n+1−1 = 15 pQHHbi M/B;2 S7/2- rQ`mb bB+?
pgen = (ppf ad)15= (r40)15 2`;B#iX
AM ##X jXR Bbi /B2 q?`b+?2BMHB+?F2Bi pgen #? M;B; pQM /2` :2M2`iBQMbiB272 M;2;2#2MX 6Ƀ` /B2 :2MmB;F2Bi /2` w2HH/2i2FiBQM rm`/2M xr2B QTiBKBbiBb+?2 q2`i2 r = 0.99 mM/ r = 0.9999 M;2MQKK2MX .B2 _2bmHii2 x2B;2M- r2H+?2
>2`mb7Q`/2`mM; M 2BM2M w2HHi`+FBM;@H;Q`Bi?Kmb ;2bi2HHi r2`/2MX
0 5 10 15 20 25
0 0.2 0.4 0.6 0.8 1
:2M2`iBQM2M pgen
r= 0.9999 r= 0.99
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/B;2 aiKK# mK2 #? M;B; pQM /2` w2HH/2i2FiBQMb`i2r 2`bi2HHi rB`/X
oQ`mb;2b2ixi- D2/2 w2HH2 Bbi BM 9y "BH/2`M bB+?i#`X
9y
jXRX 62?H2`MHvb2 mM/ oHB/B2`mM; pQM w2HHi`+FBM;@.i2M
jXRXRX 62?H2` mM/ 62?H2`7Q`iT~MxmM; BM x2HHmH `2M aiKK# mK2M
.B2 q?`b+?2BMHB+?F2Bi- KBi /2` 2BM w2HHT7/ pQM 2BM2K MBp2M w2HHi`+FBM;@Mbix `2@
FQMbi`mB2`i rB`/- ? M;i /B`2Fi pQM /2` :2MmB;F2Bi /2` w2HH/2i2FiBQM #X lK /b xm p2`@
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iB2`i r2`/2M- rb b2H#bi #2B 2BM2` M;2MQKK2M2M .2i2FiBQMb`i2 2BM2` 2BMx2HM2M w2HH2 pQM r = 0.99 2BM2 ;2`BM;2 _2FQMbi`mFiBQMbr?`b+?2BMHB+?F2Bi pT7/ = 0.9940 = 0.6692`@
;B#iX .B2 `2bmHiB2`2M/2 q?`b+?2BMHB+?F2Bi p;2M- KBi /2` 2BM pQHHbi M/B;2` aiKK#mK 2`bi2HHi rB`/- Bbi BM ##X jXR 7Ƀ` xr2B QTiBKBbiBb+?2 ;2r ?Hi2 .2i2FiBQMb`i2M r = 0.99 mM/ r = 0.9999;2x2B;i mM/ p2`/2miHB+?2M- rB2 72?H2`M7 HHB; #xrX b+?r2` /B2 m7;#2 /2b w2HHi`+FBM; BbiX
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AMb;2bKi x2B;2M /B2 ##BH/mM;2M jXR mM/ jXk- r2H+?2 M7Q`/2`mM;2M M 2BM2 miQ@
KiBbB2`i2 _2FQMbi`mFiBQM pQM x2HHmH `2M :2M2HQ;B2M Ƀ#2` pB2H2 :2M2`iBQM2M ?BMr2;
;2bi2HHi rB`/X
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K2M FMM b+?QM 2BM 2BMx2HM2` 62?H2` /xm 7Ƀ?`2M- /bb 2BM2 :2M2HQ;B2 x2`#`B+?i mM/
/B2 > H7i2 HH2` o2`rM/ib+?7i2M MB+?i FQ``2Fi `2FQMbi`mB2`i r2`/2M FMMX
9R
ETBi2H jX oHB/B2`i2b w2HHi`+FBM;
62?H2`[m2HH2M
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RX _M/T`Q#H2K2X . /B2 JBF`QbFQT#BH/2` Mm` 2BM2M FH2BM2M mbb+?MBii /2` ;2@
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i`bi m7r2Bb2M- r2`/2M pQM /2` "BH/b2;K2MiB2`mM; MB+?i 2`FMMi Up;HX ##X jXjU#VVX .B2b2 62?H2` 7Ƀ?`2M xm S7/7`;K2Mi2M Q?M2 ;ɃHiB;2M L+?7QH;2` #xrX Q?M2 ;ɃH@
iB;2M oQ`; M;2` /B2 Hb HQbi 2M/ #xrXHQbi #2;BMK`FB2`i r2`/2MX
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b2 lMi2`b2;K2MiB2`mM; Bbi 2BM2 /2` ? m};bi2M 62?H2`[m2HH2M BM /2M #2i`+?i2@
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/B2 p2`b+?KQHx2M2 w2HHFQMim` #2Q#+?i2i- bQ HB2;i 2BM2 w2HHp2`b+?K2HxmM; pQ`X .B2 2MibT`2+?2M/2M S7/7`;K2Mi2 r2`/2M KBi /2K K2`;2/@6H; p2`b2?2MX
9X o2`b+?KmixmM; mM/ `i27Fi2X L2#2M /2M H2#2M/2M w2HH2M- /B2 #2Q#+?i2i r2`/2M- H bbi 2b bB+? MB+?i p2`?BM/2`M- /bb bB+? MQ+? r2Bi2`2 P#D2Fi2 BM /2M EmH@
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#2r2;2M bB+? BK o2`;H2B+? xm /? `2Mi2M w2HH2M b2?` b+?M2HH- / bB2 bB+? 7`2B BK w2HHK2/BmK #2r2;2M mM/ bQKBi pQM /2` 6HB2Ľ;2b+?rBM/B;F2Bi /2b w2HHK2/BmKb /B`2Fi #22BM~mbbi r2`/2M Up;HX ##X jXjVX .B2b2 P#D2Fi2 r2`/2M BM /2M h`+FBM;@
.i2M Hb Fm`x2 S7/7`;K2Mi2 Q?M2 2BM2M ;ɃHiB;2M M7M; Q/2` 2BM ;ɃHiB;2b 1M/2 UHQbi #2;BM mM/HQbi 2M/V 2`FMMiX
M?M/ /2` ;2;2#2M2M "BH/b2`B2M FƺMM2M /B2b2 62?H2`[m2HH2M H2B+?i B/2MiB}xB2`i mM/
/2}MB2`i r2`/2MX lK bB2 xm [mMiB}xB2`2M mM/ xm MHvbB2`2M r2`/2M #2` pQHHbi M@
/B;2 _272`2Mx/i2M #2MƺiB;i- BM /2M2M /B2 FQ``2Fi2M #xrX FQ``B;B2`i2M w2HHFQMim`2M HH2` aiKK# mK2 2Mi?Hi2M bBM/X AM /2K M +?bi2M #b+?MBii rB`/ 2BM :2M2HQ;Bb+?2b JQ/2HH 2MirQ`72M- r2H+?2b 2b 2`Kƺ;HB+?i- /B2 62?H2`7`2B?2Bi /2` .i2M KBi 2BM2` EQM@
bBbi2MxT`Ƀ7mM; xm p2`B}xB2`2MX q2Bi2`?BM H bbi /B2 p2`r2M/2i2 .i2Mbi`mFim` 2BM2 AMi2@
;`Bi ibT`Ƀ7mM; xm- /B2 Hb :`mM/H;2 7Ƀ` /B2 1`bi2HHmM; pQM pHB/B2`i2M _272`2Mx/i2M
;2Mmixi rB`/X
9k
jXRX 62?H2`MHvb2 mM/ oHB/B2`mM; pQM w2HHi`+FBM;@.i2M
##BH/mM; jXjX, 62?H2`[m2HH2M BM w2HHi`+FBM;@ax2M`B2MX UV _M/Xwr2B w2HH2M p2`@
Hbb2M /2M #2Q#+?i2i2M "2`2B+? U/2` "BH/`M/ Bbi m7 /2` `2+?i2M a2Bi2 Hb ;`m2`
"HF2M /`;2bi2HHiVX Mb+?HB2Ľ2M/ rM/2`M xr2B M2m2 w2HH2M BM /B2 m7M?K2M- #2`
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pQM /2` "BH/b2;K2MiB2`mM; 2`FMMi r2`/2MX U+V o2`b+?KQHx2M2 w2HHFQMim`2MX GB2@
;2M 2BMB;2 w2HH2M b2?` /B+?i #2B2BMM/2`- r2`/2M /B2 w2HH2M Hb 2BM2 w2HHFQMim` 2`FMMi-bQ /bb 2b MB+?i BKK2` Kƺ;HB+? Bbi- /B2 w2HH2M 2BM/2miB; xm i`2MM2MX U/V o2`mM`2BMB@
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62?H2` p2`K2B/2M mM/ 2`F2MM2M, 1pHmB2`mM; mM/ oHB/B2`mM;
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