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Coming back to the situation of a measurement, we now introduce -

according to GUM - the two definitions:

1) The

best estimate

of the

value of the measurand

is determined from

How uncertainty is determined

its

expectation value

with respect to its associated probability density

distribution.

If this distribution is not known, it can be

estimated as the mean value

from a random sample obtained from repeated measurements.

2) The

standard uncertainty

u of the value of the measurand is determined

as the

positive root of the variance

with respect to its associated

probability density distribution.

If this distribution is not known, the

estimate of the variance of the

mean value

can be used instead.

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