24 Some functions on the probability simplex. Let x be a real-valued random variable which takes values in {a1,..., an} where a1 < a2 < . < an, with prob(x = ai) = Pi, i = 1, ..., n. For each of the following functions of p (on the probability simplex {p E R | 1"p = 1}), determine if the function is convex, concave, quasiconvex, or quasicon- cave. (a) Ex. (b) prob(x > a). (c) prob(a

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