Question: Assume that a continuous valued rv Z has a probability density that is 0 except over the interval [A, +A]. (a) Show that the differential

Assume that a continuous valued rv Z has a probability density that is 0 except over the interval [A, +A].

(a) Show that the differential entropy h(Z) is upper bounded by 1+log2A.

(b) Show that h(Z) = 1 + log2A if and only if Z is uniformly distributed between A and +A.

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