where Tin is a random variable which represents the time of interception of one information package and Tout represents the
time of transfer of the same package. We assume that E(Tout) = 1, which means that the packages are emitted immediately.
Because of the above assumptions, the measure of information processing intensity is:
ρ =
|E(Iout − Iin)|
E(T )
. (2)
We assume that E(Iin) = 0. This assumption can be interpreted as filter calibration. We denote by a the data cut-off
(rejection) parameter (if the information measure of the information package is less than a then such a package is rejected).
The number a does not reflect any physical property. Our model is an abstraction of the investigated problem. An analogy
can be discerned here to classical acoustic filters (electronic or mechanical). There exists a boundary frequency (amplitude)
such that the filter blocks the signal below (or above) it.
We assume that the symbol (sentence) is equal to 1 if the sentence is true. In other cases it is equal to 0 (Iverson bracket).
We denote by q the probability of rejection and by p the probability of interception of the information package (of course,
there is always (p + q = 1)):
q := E([x < a]) =
a
−∞
pdfγ (x + m)dx,
p := E([x ≥ a]) =
∞
a
pdfγ (x + m)dx,