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Subject:

joint and conditional distributions

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Date:

Tue, 12 Jan 1999 15:19:15 -0600

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 I have a following problem. I am sorry if the problem is trivial... Let us have a conditional distribution p(X) = \product_{i} P(L_i | R_i), where L_i are disjoint subsets of variables from X=(X_0,...,X_{n-1}), each X_j is in some of L_i subsets, and R_i is a subset from L_0 U ... U L_{i-1}. Does there for each such distribution exist a joint probability distribution where the sets L_i has to be of cardinality 1 only? If not, why? Is there a simple counter example? An example of what I am saying is that for instance we have p(ABC)=p(AB|C). Isn't p(ABC)=p(C)p(A|C)p(B|AC) equivallent to p(AB|C)? thank you for your soon asnwer Martin %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%