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④
Frequently, the probability density f(x) of the stochastic quantity X is not
exactly known.
The only information which may be available is a sample of N
random
realizations
of X, namely X
1
, X
2
, X
3
, …. X
N
.
In this case, the value of the two most important expectation values can only
5.2
be
estimated
based on the random sample:
a) estimate for
ξ
: , i.e. the mean value;
1
1
X
N
i
i
X
N
=
=
∑
b) estimate for
σ
2
:
63
(
)
2
2
1
1
1
N
i
i
s
X X
N
=
=
−
−
∑