Exercise 2.6 - Conditional Independence

Answers

In question (a), we have:

Pr ( H | e 1 , e 2 ) = Pr ( H ) Pr ( e 1 , e 2 | H ) Pr ( e 1 , e 2 ) .

Thus the answer is (ii).

For question (b), we have the further decomposition:

Pr ( H | e 1 , e 2 ) = Pr ( H ) Pr ( e 1 | H ) Pr ( e 2 | H ) Pr ( e 1 , e 2 ) .

So both (i) and (ii) and sufficient. Moreover, we have:

Pr ( e 1 , e 2 ) = H Pr ( e 1 , e 2 , H ) = H Pr ( H ) Pr ( e 1 | H ) Pr ( e 2 | H ) .

so (iii) is sufficint as well since we can calculate p ( e 1 , e 2 ) from scratch.

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2021-03-24 13:42
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