Dose 2016

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:

N

1

∑

a) estimate for ξ : , i.e. the mean value;

X

X

=

i

N

i

1

=

N

1

) 2

(

∑

2

s

X X −

b) estimate for σ 2 :

=

i

N

1

−

i

1

=

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