Inference and independence (a) 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 them. 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(x1|y ) and p(x2|y ) ii. p(x1, x2), p(y ) and p(x1, x2|y ) iii. p(x1|y ), p(x2|y ) and p(y ) iv. p(x1), p(x2) and p(x1, x2|y ) v. p(x1), p(x2), p(x1|y ) and p(x2|y ) (b) now suppose you know that (x1 ⊥⊥ x2|y ). now, which of the sets before are sufficient? justify. as before