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,Jensens incequality 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. ce) Follows by Chebyshev's inequality. The correct answer is

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,Jensens incequality 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. ce) Follows by Chebyshev's inequality. The correct answer is

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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