3.24 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 = a;) = 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. (а) Ех. (b) prob(x > a). (c) prob(a
3.24 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 = a;) = 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. (а) Ех. (b) prob(x > a). (c) prob(a
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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