Civil Engineering Reference
In-Depth Information
a)
N independent short term realisations
b)
The probability of mean values
Fig. 2.4
Ensemble statistics of mean value recordings
There is no reason why
τ
may not attain negative as well as positive values, and
since
( )
(
)
(
)
( )
(
)
(
)
E xt xt
E xt
xt
E xt
xt
⎡
⋅
−=
τ
⎤ ⎡
−⋅
τ
⎤ ⎡
=
−⋅
τ
−+
τ
τ
⎤
⎦
(2.18)
⎣
⎦ ⎣
⎦ ⎣
then
()
( )
Cov
τ
Cov
τ
(2.19)
=
−
x
x
Cov
is symmetric with respect to its variation with
Thus,
τ
.
x
