P00
μw´2 P(1 - P)(1 - 2P)
h1+μw P (1—P )]3
Second, we wish to compute g0 and g00. Recall that the solution of the equation
Piw = Pid is unique and denoted by: pi = gi (wi). We have:
Pkd
exp
-pk-ΛdPkd
μd
P exp ' ,
1...n
so that, using the same reasoning as above:
dpi _ -Td Pd (1 - Pd)
----- —--:—;---------------—
dpi 1 + ΛdPid (1 - P
Differentiation of the expression Piw - Pid —0, as a function of wi leads to
dPw dPid dpi _0
dwi dpi . dwi ,
thus (using again the condition Piw — Pid):
g0
dPw
dwi
^dPd
dpi
. 1 + Λd Pid (1 - d'
μw 1 + — Piw (1 - Piw )
(60)
Therefore:
g00
μd
μw
Γ "I 2 ,
[1 + Λw Piw (1 - Piw)]
with
'" (1 - 2Pi^ dPd g0 ×
μd κ d dpi
Λw
1 + PW Pw (1 - Pw )
μ
Λw dPw
- — (1 - 2Pw ) dP- ×
μw dwi
Λd
1 + τd Pd (1 - Pd)
μ
After simplification, we get:
1 μ Λd Λw \
μw ∖μd μw )
(1-2P)P(1-P)
[1 + Λw P (1 - P )]
33
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