In article <[EMAIL PROTECTED]>,
Alan McLean <[EMAIL PROTECTED]> wrote:
>'Height of an individual' is only a random variable when the selection
>of the individual and the measurement of his or her height is still in
>the future. The full name of the variable is 'Height of a randomly
>chosen individual'!
No, this can even be the case if it is in the past, as long
as it is not previously known.
Also, randomness is NOT restricted to some means of "random
sampling" from a "population". This is ONE way of arriving
at situations about which probability statements can be
made, but is not the only one, and the others are of much
greater importance.
>So if you take a random sample of adult males, each individual is
>selected randomly, and the resultant measurement can vary over the
>population of all males. This is true for a single observation and for
>each of n observations.
One could use probability just as well on historical records
of supernovas, assuming that these have not already been used
for inference.
Selecting individuals at random from populations is not the
only way of getting probability models. Using past sunspot
data to try to get a model of solar activity, and recognizing
that random processes were involved, is a proper use of
probability. Similar ones occur in discussing such things
as global warming or epidemics.
Independence and identical distributions are STRONG prior
assumptions, much stronger than can be made by observing
relative frequencies.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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