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CS CS 47100- Probabilistic Inference and Independence

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2. (6 pts) Probabilistic Inference and Independence (a) (3 pts) Let X1, X2 and Y be random variables. We want to calculate P(Y| X1, X2) but we do not possess any independence/conditional independence ... information about these variables. For each of the following sets of distributions show how to calculate the desired query or explain why it is not possible: i. P(X1, X2), P(Y), P(Xi|Y) and P(X2|X1) ii. P(X1, X2), P(Y) and P(X1, X2|Y) iii. P(X] |Y), P(X2|Y), P(X1, X2) and P(Y) iv. P(X1), P(X2), P(X1, X2) and P(X1, X2|Y) v. P(X]), P(X2), P(X1, X2|Y) and P(X,| Y) (b) (3 pts) Now suppose you know that (X1 IL X2|Y). Now, which of the aforementioned sets are sufficient? Justify your answers. [Show More]

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