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Suppose we have two variables Y and Z that depend on a third one, X. We are given P(x), P(y|x) and P(z|x). The joint probability distribution P(x,y,z), according to the chain probability rule, is given by P(x,y,z) = P(x)P(y|x)P(z|x,y)

But how can we compute P(z|x,y) with the given data?

Since Y does not depend on Z directly I "feel" that P(z|x,y) = P(z|x)(Px) but I can't find a logical reason for it.

Can you lend me a hand?

Thank you for your time.

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# Explicit joint probability distribution.

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