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R e
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o p y
()221
2()0S S S FS f S S FS
µ        =
>
(1)
R e
v i e w
C
o p y
()ds s c FS
FS
=
22221exp 21
µ
(2)
In (1)-(2),  2is the variance of the Gaussian pdf (before truncation) a nd µis its mean value. The probability of S not exceeding the transition level T k is
()()
Pr T k
k k F T S T = (3)
For simplicity in notation F will be used for the probability distribution function F Tk
throughout this paper, that is F (T k )=F Tk (T k ). The distribution function of T k is obtained
from (1)-(2) and is described by
+=      2
22121 µ µk k T erf c T F (4)
where erf (·) denotes the error function. One may note that when FS  grows (that is, FS
tends to infinity) the quantity c in (2) tends to unity and thus (1) and (4) correspond to the standard probability density and distribution for a Gaussian stochastic variable – quantities that in the sequel will be denoted  and  ,respectively.

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