3. (24 points) Given a set of probabilities P = [p1, p2, , ] for each nonnegative pi ≥ 0, I ≤ i ≤n, and the (Shannon) entropy is defined by H (P) = .
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] for each nonnegative pi ≥ 0, I ≤ i ≤n, and 
the (Shannon) entropy is defined by H (P) =
.