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Conditional Independence [2 P]

a)
Construct a probability distribution P(A,B,C) that disproves

$\displaystyle {\bf P}(A,B) = {\bf P}(A) {\bf P}(B) \rightarrow
{\bf P}(A,B\vert C) = {\bf P}(A\vert C) {\bf P}(B\vert C) .$

Illustrate the phenomenon of 'explaining away'.

b)
Construct a probability distribution P(A,B,C) that disproves

$\displaystyle {\bf P}(A,B\vert C) = {\bf P}(A\vert C) {\bf P}(B\vert C) \rightarrow
{\bf P}(A,B) = {\bf P}(A) {\bf P}(B) .$



Haeusler Stefan 2007-12-03