�� 1DPH��BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB����9HQQ�'LDJUDPV�6KRZLQJ�3UREDELOLWLHV�'DWH�����7LPH��7RWDO�PDUNV�DYDLODEOH��7RWDO�PDUNV�DFKLHYHG��BBBBBB���������������������

�

�

4XHVWLRQV4�������������

Solutions

�D��6WDWH�LQ�ZRUGV�WKH�UHODWLRQVKLS�EHWZHHQ�WZR�HYHQWV�5�DQG�6�ZKHQ�3�5ಭ6�� ��

���

7KH�HYHQWV�$�DQG�%�DUH�LQGHSHQGHQW�ZLWK�3�$�� � �DQG�3�$ಮ%�� �

)LQG

�E��3�%�

���

�F��3�$ಭ%�

���

�G��3�% $�

���

�7RWDO���PDUNV�

4�������������

-DNH�DQG�.DPLO�DUH�VRPHWLPHV�ODWH�IRU�VFKRRO�7KH�HYHQWV�-�DQG�.�DUH�GHILQHG�DV�IROORZV

-� �WKH�HYHQW�WKDW�-DNH�LV�ODWH�IRU�VFKRRO

.� �WKH�HYHQW�WKDW�-DNH�LV�ODWH�IRU�VFKRRO

3�-��� �������3�-�ಭ�.�� ������DQG�3�-��ಭ�.�� ����

2Q�D�UDQGRPO\�VHOHFWHG�GD\��ILQG�WKH�SUREDELOLW\�WKDW

�D���DW�OHDVW�RQH�RI�-DNH�RU�.DPLO�DUH�ODWH�IRU�VFKRRO�

���

�E���.DPLO�LV�ODWH�IRU�VFKRRO�

���

*LYHQ�WKDW�-DNH�LV�ODWH�IRU�VFKRRO�

�F���ILQG�WKH�SUREDELOLW\�WKDW�.DPLO�LV�ODWH�

���

7KH�WHDFKHU�VXVSHFWV�WKDW�-DNH�EHLQJ�ODWH�IRU�VFKRRO�DQG�.DPLO�EHLQJ�ODWH�IRU�VFKRRO�DUH�OLQNHG�LQVRPH�ZD\�

mutually exclusive

3 I IP A xPCB P Arb 12

Let PCB se

xx x Iiz4 5 55 30L 122 5

9 5 9 se I 36 36 129 12

5 3612 Ia Iz I

36

I9

to 15 05

J K70

0.3

0.2

0.1507.2 GI

�G���'HWHUPLQH�ZKHWKHU�RU�QRW�-�DQG�.�DUH�VWDWLVWLFDOO\�LQGHSHQGHQW�

���

�H���&RPPHQW�RQ�WKH�WHDFKHUV�VXVSLFLRQ�LQ�WKH�OLJKW�RI�\RXU�FDOFXODWLRQ�LQ��G��

���

�7RWDO���PDUNV�

4�������������

�D���*LYHQ�WKDW�3�$�� �D�DQG�3�%�� �E�H[SUHVV�3�$�ಮ�%��LQ�WHUPV�RI�D�DQG�E�ZKHQ

�L��$�DQG�%�DUH�PXWXDOO\�H[FOXVLYH�

�LL��$�DQG�%�DUH�LQGHSHQGHQW�

���

7ZR�HYHQWV�5�DQG�4�DUH�VXFK�WKDW

3�5�ಭ�4v��� ����������3�4�� ������DQG�3�5_4�� ����

)LQG�WKH�YDOXH�RI

�E���3�5�ಮ�4��

���

�F���3�5�ಭ�4��

���

�G���3�5��

���

�7RWDO���PDUNV�

4�������������

*LYHQ�WKDW

3�$�� ��������3�%�� ������DQG�3�$�ಭ�%�� �����

ILQG��$�ಮ�%�

���

�E��3��$ଐ�_�%ଐ�

���

P J XP K 0.25 0.2 0 05 f 0.15 P JnkSo not independent

suspicion seems to be correct

P AUB a bP AUB PCA PCB P Arb

a t b ab

PCRIQ P RnQ O I PRnaPCQ O 35

0.515 035 315

0.035R 5 Q

O 185

0.67

33 22 13 32t.gg I

533

7KH�HYHQW�&�KDV�3�&�� �����

7KH�HYHQWV�$�DQG�&�DUH�PXWXDOO\�H[FOXVLYH�DQG�WKH�HYHQWV�%�DQG�&�DUH�LQGHSHQGHQW�

�F��)LQG�3�%�ಭ�&�

���

�G��'UDZ�D�9HQQ�GLDJUDP�WR�LOOXVWUDWH�WKH�HYHQWV�$��%�DQG�&�DQG�WKH�SUREDELOLWLHV�IRU�HDFK�UHJLRQ�

���

7RP�LQYLWHV�$YLVKD�WR�SOD\�D�JDPH�ZLWK�WKHVH�GLFH�

�H��)LQG�3�>%�ಮ�&@ଐ�

���

�7RWDO����PDUNV�

4�������������

)LJXUH��

7KH�9HQQ�GLDJUDP�LQ�)LJXUH���VKRZV�WKUHH�HYHQWV�$��%�DQG�&�DQG�WKH�SUREDELOLWLHV�DVVRFLDWHGZLWK�HDFK�UHJLRQ�RI�%��7KH�FRQVWDQWV�S��T�DQG�U�HDFK�UHSUHVHQW�SUREDELOLWLHV�DVVRFLDWHG�ZLWK�WKHWKUHH�VHSDUDWH�UHJLRQV�RXWVLGH�%�

7KH�HYHQWV�$�DQG�%�DUH�LQGHSHQGHQW�

�D���)LQG�WKH�YDOXH�RI�S�

���

*LYHQ�WKDW�3�%�_�&�� �

�E���ILQG�WKH�YDOXH�RI�T�DQG�WKH�YDOXH�RI�U�

���

PCB Pcc45 0.2 0.09

o.aeI

PCA xP B P AnBPto 11 0.4 o I p 0.15Pto 1 01 0.25

0.4

P Bnc5qtl 2.2

9 0.2 5q 1.2q O 24

r 0.41 0.151 0.24 0.21 0.21

�F���)LQG�3�$�ಮ�&�_�%��

���

�7RWDO���PDUNV�

�

4�������������

)RU�WKH�HYHQWV�$�DQG�%�

3�$�ಭ�%�� ������DQG�3�$�ಭ�%�� �����

�D��)LQG�3�$��

���

�E��)LQG�3�$�ಮ�%��

���

*LYHQ�WKDW�3�$�_�%�� ����

�F��ILQG�3�$�ಭ�%��

���

�G��'HWHUPLQH�ZKHWKHU�RU�QRW�$�DQG�%�DUH�LQGHSHQGHQW�

���

�7RWDO���PDUNV�

�

4�������������

$�DQG�%�DUH�WZR�HYHQWV�VXFK�WKDW

3�%�� ��ଢ������3�$�_�%�� ��ଢ������3�$�ಮ�%�� ���ଢ��

�D��)LQG�3�$�ಭ�%��

���

�E��'UDZ�D�9HQQ�GLDJUDP�WR�VKRZ�WKH�HYHQWV�$��%�DQG�DOO�WKH�DVVRFLDWHG�SUREDELOLWLHV�

���

)LQG

�F��3�$�

0 lt I 0.750.4 4

27 33 22x

18

P A I 0.18 0.22 0.6

P AUB I 0.18 0.82

P Arb xPCB xt 0.22

0.6 0.132 1 0.1320.132 0 42 0.4 0.33

P Arb 0.33PCA PCB P Arb0.6 x 0.55

0.33 0.33

independent

P AIB P AaB P Arb Plans PCBI RBI Ext Is5

3 s I20 10

Zo tf Io Io

���

�G��3�%�_�$�

���

�H��3�$�ಭ�%�

���

�7RWDO���PDUNV�

�

4�������������

7KH�9HQQ�GLDJUDP�VKRZV�WKH�SUREDELOLWLHV�RI�FXVWRPHU�ERRNLQJV�DW�+DUU\V�KRWHO�

5�LV�WKH�HYHQW�WKDW�D�FXVWRPHU�ERRNV�D�URRP

%�LV�WKH�HYHQW�WKDW�D�FXVWRPHU�ERRNV�EUHDNIDVW

'�LV�WKH�HYHQW�WKDW�D�FXVWRPHU�ERRNV�GLQQHU

X�DQG�W�DUH�SUREDELOLWLHV�

�D���:ULWH�GRZQ�WKH�SUREDELOLW\�WKDW�D�FXVWRPHU�ERRNV�EUHDNIDVW�EXW�GRHV�QRW�ERRN�D�URRP�

���

*LYHQ�WKDW�WKH�HYHQWV�%�DQG�'�DUH�LQGHSHQGHQW

�E���ILQG�WKH�YDOXH�RI�W

���

�F���KHQFH�ILQG�WKH�YDOXH�RI�X

���

�G���)LQG

f x 2,1

I10

0

PCB x PCD P BND6 x C 42 E 0.2742 t E 0.27

I 0.45

C 0.03U l f 33 1.27 1.15 t 03 0.22

u 0.22

�L���3�'_5�ಭ�%�

�LL���3�'_5�ಭ�%ଐ��

���

$�FRDFK�ORDG�RI����FXVWRPHUV�DUULYH�DW�+DUU\V�KRWHO�

2I�WKHVH����FXVWRPHUV

���KDYH�ERRNHG�D�URRP�DQG�EUHDNIDVW

���KDYH�ERRNHG�D�URRP�ZLWKRXW�EUHDNIDVW

�H���(VWLPDWH�KRZ�PDQ\�RI�WKHVH����FXVWRPHUV�ZLOO�ERRN�GLQQHU�

���

�

�7RWDO�IRU�TXHVWLRQ� ����PDUNV�

�

Powered by TCPDF (www.tcpdf.org)

27To 0.45

1537

40 0.45 t 37 x37

18 1 15

33