Question: Consider an HMM with state variables {X i } and emission variables {Y i }. (i) [True or false] X i is always conditionally independent

Consider an HMM with state variables {X_i} and emission variables {Y_i}.

(i) [True or false] X_i is always conditionally independent of Y_i+1 given X_i+1.

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

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

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