(5) (5 points) Choose the expressions that is equal to 1, no assumptions: (i) $\sum_a P(A = a|B)$ (ii) $\sum_a \sum_b P(A = a|B = b)$ (iii) $\sum_b P(A = a|B = b)$ (iv) $\sum_a P(A = a)P(B = b)$
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(i) $\sum_a P(A = a|B)$: This is the sum of conditional probabilities of A given B over all possible values of A. By the law of total probability, this sum is equal to 1. (ii) $\sum_a \sum_b P(A = a|B = b)$: This expression sums the conditional probability of A Show more…
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