Let X be a positive random variable; i.e., P(X 0) = 0. Argue that (a) E(1/X)

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Let X be a positive random variable; i.e., P(X ≤ 0) = 0. Argue that
(a) E(1/X) ≥ 1/E(X)
(b) E[−log X]≥ −log[E(X)]
(c) E[log(1/X)] ≥ log[1/E(X)]
(d) E[X³] ≥ [E(X)]³.

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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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Question Posted: Oct 13, 2022 02:25 AM

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Let X be a positive random variable; i.e., P(X 0) = 0. Argue that (a) E(1/X)

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a E1X 1EX The first part of this is to show that the expectation of a ratio is greater than that of its first term The second part is to show that the expected value of a random variable X is greater ...View the full answer

Introduction To Mathematical Statistics

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