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If we flipped a fair coin 1000 times,
it is unlikely that we would get exactly 500 heads and 500 tails.
More likely the number of heads would lie somewhere between
400 and 600.
Or would it lie in another range?
The theoretical value, called the ``**mean**" or the
``**expectation**," is 500.
The value from our experiment in actually flipping a fair coin
is called the ``**sample mean**.''
How much difference should we expect
between the sample mean and the true mean *m*?
Both the coin flips *x* and our sample mean are *random variables*.
Our 1000-flip experiment could be repeated many times and would
typically give a different each time.
This concept will be formalized
in section 11.3.5. as
the ``**variance of the sample mean**,'' which is
the expected squared difference between the true mean
and the mean of our sample.
The problem of estimating the **statistic**al parameters of
a time series, such as its mean, also appears in seismic
processing. Effectively, we deal with seismic traces of
finite duration, extracted from infinite sequences whose
parameters can only be estimated from the finite set of
values available in these seismic traces. Since the
knowledge of these parameters, such as signal-to-noise
ratio, can play an important role during the processing,
it can be useful not only to estimate them, but also
to have an idea of the error made in this estimation.

** Next:** Ensemble
** Up:** Resolution and random signals
** Previous:** Bandlimited noise
Stanford Exploration Project

10/21/1998