Page 83, 1.10.7.* Let X be a positive random variable; i.e., P (X ≤ 0) = 0. Argue that (a) E(1/X³) ≥ 1/{E(X)}³ (b) E[X4] ≥ [E(X)]4. >

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Page 83, 1.10.7.* Let X be a positive random variable; i.e., P (X ≤ 0) = 0. Argue that
(a) E(1/X³) ≥ 1/{E(X)}³
(b) E[X4] ≥ [E(X)]4.
Transcribed Image Text:Page 83, 1.10.7.* Let X be a positive random variable; i.e., P (X ≤ 0) = 0. Argue that (a) E(1/X³) ≥ 1/{E(X)}³ (b) E[X4] ≥ [E(X)]4.
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