Question: Let X be a random variable taking on n values with probabilities p1, p2, . . . , pn. Recall from Lecture 9 that the

Let X be a random variable taking on n values with probabilities p1, p2, . . . , pn. Recall from Lecture 9 that the min-entropy of X, denoted E(X), is given by

Let X be a random variable taking on n values with probabilities

If X is uniformly distributed then p1 = p2 = = pn = 1 .

(a) Show that if X is not uniformly distributed then necessarily one of the pi s is > 1.

(b) Show that if X is not uniformly distributed then E(X)

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