In article <[EMAIL PROTECTED]>,
dennis roberts <[EMAIL PROTECTED]> wrote:
>we memorize defintions of terms don't we? most feel that is helpful ... so,
>same thing applies to many formulas too ... and, if one uses then enough
>... they usually CAN'T help but memorize them ...
Most of the time, we should not be using "definitions" but
characterizations.
What is the difference? The difference is that there can
only be one definition, but there can be many good
characterizations. This is quite important, as in many
cases, the usual definitions are nothing more than a bad
selection of concisely stated properties, without any
attempt at understanding, to be memorized but with less
hope of understanding than if not made in the first place.
We need some definitions, so we know what we are talking
about, but only those. It is necessary to define parameter
of a distribution (anything which can be determined by the
distribution), cumulative distribution function,
probability mass function, density. The usual definitions
of independence and expectation found in textbooks should
be replace by other characterizations, and these relegated
to computational procedures, very definitely not as
representations of the underlying concept. If fact, while
expectation can be computed from the distribution of the
random variable, it should not be defined from that.
The concepts are not that much harder, but seem to become
much harder AFTER the routine is learned.
--
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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