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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 45E
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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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