(13) Let X be a random variable that takes only positive values. If E|X| < ∞, prove that E(X) · E(1/X) > 1. (a) Since f (t) = 1/t is a convex function for t > 0, Jensen's inequality gives that E(1/X) > 1/E(X). (b) Since f(t) = 1 = tlt is a convex function for t > 0, Jensen's inequality gives that E(1/X) > 1/E(X). (c) The statement of the problem is, in fact, false. (d) Follows by Markov's inequality (e) Follows by Chebyshev's inequality. The correct answer is (a) (b) (c) (d) (e) N/A (Select One)

(13) Let X be a random variable that takes only positive values. If E|X| < ∞, prove that E(X) · E(1/X) > 1. (a) Since f (t) = 1/t is a convex function for t > 0, Jensen's inequality gives that E(1/X) > 1/E(X). (b) Since f(t) = 1 = tlt is a convex function for t > 0, Jensen's inequality gives that E(1/X) > 1/E(X). (c) The statement of the problem is, in fact, false. (d) Follows by Markov's inequality (e) Follows by Chebyshev's inequality. The correct answer is (a) (b) (c) (d) (e) N/A (Select One)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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