>
> I think that introducing the word "independent" as a descriptor of
> sample spaces and then carrying it on to the events in the product space
> is much less likely to generate the confusion due to the common informal
> description "Independent events don't have anything to do with each
> other" and "Mutually exclusive events can't happen together."
>
I like Dick's idea a lot. To me, part of the problem is that textbooks
fail to distinguish independence as a mathematical construct from
independence as a modeling construct. Too many intro books put their
expository effort into the mathematical definition, and then get
obfuscatorily circular when it comes to the examples. Mathematicians
*assume* independence, statisticians look at the data, and textbooks fail
to recognize the difference. Dick's approach gives a nice way, in
an elementary seting, to help students recognize situations where an
assumption of independence is likely to stand up to empirical scrutiny.
I agree, too, Dick, that this should help with mutually exclusive
vs. independent.
George Cobb
George W. Cobb
Mount Holyoke College
South Hadley, MA 01075
413-538-2401
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