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I have expressions for marginal probability distributions p(a) and p(b). The joint probability distribution p(a,b), if I understood correctly, can be obtained by the product p(a)*p(b). I need to find the conditional probability P(Y|a,b). What information about Y is needed for doing this? If the probability distribution of Y is simply given as p(Y), what would be the expression for conditional probability?

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What is Y in terms of a and b? – oks Feb 14 at 8:34
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p(A=a,B=b) = p(A=a)*p(B=b) only if A and B are independent. – oks Feb 14 at 8:36
I am trying to understand the theory behind a specific mathematical derivation, so I am not yt sure what is Y in terms of a and b, but assuming p(Y) is known simply as p(Y) and p(a,b) = p(a)*p(b), what should be done to get P(Y|a,b)? Or is the given data not enough to determine this conditional probability? – user13267 Feb 14 at 9:33

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I need to find the conditional probability $P(Y|a,b)$. What information about $Y$ is needed for doing this?

One way or another, the joint distribution of $(Y,a,b)$.

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If $Y$ is independent of $a$ and $b$ then $$P(Y|a,b) = P(Y).$$

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it's not independent – user13267 Feb 14 at 9:30

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