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Statistics and the Wavefunction
Let's review some elementary statistics about random variables that can assume
discrete
values.
Suppose we make many repeated measurements of a random discrete variable
called x. An example of x is the mass, rounded to nearest kg, or the height, rounded to the
nearest cm, of a randomlychosen adult male.
We label the possible results of the measurements with an index i.
For instance, for
heights of adults males, we might have x
1
=25 cm, x
2
= 26 cm, etc (nobody is shorter than
25 cm).
The list {x
1
, x
2
, .
.. x
i
,... } is the called the
spectrum
of possible measurement
results.
Notice that x
i
is
not
the result of the i
th
trial (the common notation in statistics
books).
Rather, x
i
is the i
th
possible result of a measurement in the list of all possible
results.
N = total # of measurements.
n
i
= # times that the result x
i
was found among the N measurements.
Note that
where the sum is over the
spectrum
of possible results,
not
over the
N different trials.
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 Fall '08
 STEVEPOLLOCK
 Mass, Probability theory, #, 25 cm, Michael Dubson

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