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Since the distribution of escape times is, apart from at very small times, exponential, it can be characterised simply by its expected value.
As a result, the conductivity is commonly modeled as a spatial random field, defined by its expected value and a covariance function.
In this setting, the life-cycle cost is uncertain and can be quantified by its expected value over the space of the uncertain parameters for the structural and excitation models.
Description of the uncertainty for these characteristics and for the predictive relationships, by appropriate probability distributions, leads then to quantification of the life-cycle seismic losses by its expected value.
Earlier we saw that all consequentialists now accept that assessing each act individually by its expected value is in general a terrible procedure for making moral decisions.
For the RLS-type algorithms with the fixed forgetting factor, we have the ergodicity assumption for P k,i [6, 7, 27], that is, the time average of a sequence of random variables can be replaced by its expected value so as to make the analysis for the performance of these algorithms tractable.
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where z is complex, Gaussian distributed with the variance σ N 2. We simplify the following analysis by approximating Pmax with its expected value, given a certain variance: P peak ≈ E max Per ( n 0, m 0 ) = P Rx · NM + σ N 2. (13).
The probability that YΛ deviates from its expected value by a positive amount decays exponentially with the area of Λ, while the probability that it deviates from its expected value by a negative amount decays exponentially with the perimeter of Λ.
The basic premise of the new leveling method is that each correction is calculated to minimize the difference between the measurement and its expected value determined by its neighboring data, yet the correction should be a slowly varying function of time.
Fortunately, in the linear-quadratic Gaussian case, i.e., where the system is linear and the errors of the sensors and perception model are assumed to be Gaussian, the optimal control can still be calculated very similarly to the previous case as in Equation 22, by merely replacing s τ with its expected value, u * ( s τ ) = L * E [ s τ ]. (25).
where R n is the regional power spectrum of the synthetic data and E{R n } its expected value as given by Eq. 19.
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Justyna Jupowicz-Kozak
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