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(a) E(- log X) > – log(EX) (b) E[log(1/X)] > log[1/EX] (c) E (X³) > (EX)³

(a) E(- log X) > – log(EX) (b) E[log(1/X)] > log[1/EX] (c) E (X³) > (EX)³

A First Course in Probability (10th Edition)
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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5. Let X be a positive random variable; i.e., P(X < 0) = 0. Show that (a) E(- log X) > - log(EX) (b) E[log(1/X)] > log[1/EX] (c) E (X³) > (EX)³
Transcribed Image Text:5. Let X be a positive random variable; i.e., P(X < 0) = 0. Show that (a) E(- log X) > - log(EX) (b) E[log(1/X)] > log[1/EX] (c) E (X³) > (EX)³
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