High Quality Content by WIKIPEDIA articles! One may also define the perplexity of a random variable X as the perplexity of the distribution over its possible values x. It is easy to see that in the special case where p models a fair k-sided die (a uniform distribution over k discrete events), its perplexity is k. We may therefore regard any random variable with perplexity k as having the same uncertainty as a fair k-sided die. We are "k-ways perplexed" about the value of such a random variable. (Unless it is also a fair k-sided die, more than k values will be possible, but the overall uncertainty is no greater because some of these values will have probability greater than 1/k.)

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