Question: Let (x) be a binary variable with outcomes 0 and 1 . Let (p=operatorname{Pr}(x=1)). Show that entropy has the maximum at (p=0.5).

Let \(x\) be a binary variable with outcomes 0 and 1 . Let \(p=\operatorname{Pr}(x=1)\). Show that entropy has the maximum at \(p=0.5\).

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