In article <[EMAIL PROTECTED]>,
James Ankeny <[EMAIL PROTECTED]> wrote:
> Hello,
> I have a question regarding the definition of probability. If I
>understand correctly, probability may be defined using just axioms. However,
>my textbook also uses a relative frequency definition, in which a
>probability is defined as being the proportion of times an outcome occurs in
>repeated trials of an experiment. This makes sense when one flip of the coin
>is one trial, and in repeated trials, the proportion of heads is 1/2. But
>what about a situation (an ex. in my textbook) where the probability of rain
>tomorrow is 0.70. How do you define this experiment? Perhaps you measure
>rainfall, temperature, pressure, etc. for each day over a long time period.
>Then the probability of rain tomorrow is the proportion of times that rain
>occurred on days with similar values for temp., humidity, etc.? This seems a
>bit awkard to me. Also, how many trials must one perform an experiment,
>before you know that the proportion converges to a particular fraction? Any
>help on interpretation of relative frequency probabilities would be greatly
>appreciated. In many cases, it seems difficult, at least for textbook
>examples, to define what the actual experiment is.
I think it is dangerous, and even useless, to ATTEMPT to
define probability. In physics, one no longer even tries
to define length or mass, just specify their properties.
It is the same with probability. A quantum mechanical
model has a joint probability distribution for observations,
but is worse between them. Just as we use the postulated
properties for length and mass, we should use those for
probabilities. We do have the nasty problem that there
is no way we can accurately calculate probabilities, unless
very strong additional assumptions are made.
--
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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