Question: Consider an N - letter source with probabilities, Pi, i = 1, 2, 3 N. The entropy of the source is given by Prove that

Consider an N - letter source with probabilities, Pi, i = 1, 2, 3€¦ N. The entropy of the source is given by

Prove that the discrete distribution that maximizes the entropy is a uniform distribution. Hint: You need to perform a constrained optimization since the source probabilities must form a valid probability mass function, and thus p1+ p2+€¦+ pN = 1.

= -Plog (p;) |) H(p) p;log (P)

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