Question: 22. (a) Suppose that f (x) = xm, where m is a positive integer, and X is a random variable taking values x1, x2, .

22.

(a) Suppose that f (x) = xm, where m is a positive integer, and X is a random variable taking values x1, x2, . . . , xN ≥ 0 with equal probabilities, and where the sum x1 + x2 + · · · + xN = 1. Deduce from Jensen’s inequality that XN i=1 f (xi ) ≥ N f (1/N).

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