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Show that H(X) log|X | for any distribution pX . Conclude that for random variables taking values in [n] := {1, . . . ,
Show that H(X) log|X | for any distribution pX . Conclude that for random variables taking values in [n] := {1, . . . , n}, the distribution which maximizes H(X) is Uniform([n]). Hint: log is a convex function
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Mathematical Interest Theory
Authors: Leslie Jane, James Daniel, Federer Vaaler
3rd Edition
147046568X, 978-1470465681
