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How can be proven that the entropy of a dice roll is maximized when the probability of each of its $6$ faces is equal, $1/6$?

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Suprise is defined as -log(p{X=x}). A good way to think of entropy is the "expected surprise". In this sense, its easy to see that the uniform distribution maximizes the expected surprise.

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    not sure how to do it... can you help?2012-10-26
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The entropy is given by $-\sum p_i\ln p_i$. Use Jensen's inequality with the logarithm function.

  • 0
    not sure how to do it... can you help?2012-10-26