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------- Additional Comments From [EMAIL PROTECTED]  2005-08-17 21:18 -------
I think you're right. it is coming from the accumulation of numerical error. but
I think the solution should be more complicated than a simple short circuit.
let's see an example again:

if we calculate cumulativeProbability(50) for (6000, 200, 100), the upper tail
(X>=50) probability will be 1 - cumulativeProbability(50) = 3.37E-11. but if you
do a sum of the point probabilities using probability(50),(51),...,(100), which
by textbook definition defines the upper tail, you'll get 6.02E-49. 
the discrepency, coming from the accumulation of numerical error, results in a
false estimate of the real cumulative probability, by a factor of E38. true,
both are very small, but in some cases it would matter for sure. 

that's why my suggestion is, either we define a new function to the class to
calculate P(X>=x) for upper tail probability, or we can define the
cumulativeProbability so that it calculates P(m<=x<=n); in this case if you
simply want upper or lower tail, just define m or n separately. and I guess
it'll help to short-circuit the class so that it won't produce p>1 or p<0 cases.

what do you think?

(In reply to comment #2)

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