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September 25th, 2008, 02:18 AM   #1
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Please help what term to use

Please help what term to use for the following issue.

Given a set X = { x1, x2, ..., x_n } and a probability distribution on it P (X) = { p (x1), p (x2), ..., p (x_n) }.

Given a division of the set ? on non-overlapping subsets ?1, ?2, ... ?_m, so:
X1 U X2 U ... U X_m = X

Is there a term for the probability distribution on the set of the subsets X' = { X1, X2, ..., X_m }:

P (X') = { p (X1), p (X2), ..., p (?_m) }, where p (Xi) - the sum of probabilities of all x in Xi?

Thank you in advance.
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September 25th, 2008, 08:29 AM   #2
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Re: Please help what term to use

I'm not sure entirely. If X1, ..., Xm partition X, then the total probability is still 1.

I don't know if there's a special term for the other probability distribution.
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