Consider an HMM with state variables {X i } and emission variables {Y i }. (i) [True

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Consider an HMM with state variables {Xi} and emission variables {Yi}. 

(i) [True or false] Xi is always conditionally independent of Yi+1 given Xi+1

(ii) [True or false] There exists an HMM where Xi is conditionally independent of Yi given Xi+1

(iii) [True or false] If Yi = Xi with probability 1, and the state space is of size k, then the most efficient algorithm for computing p(X|y1 · · · , yt) takes O(k) or less time.

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