Compare the problem in Exercise 54 with that in Exercise 45. Exercise 45 It is known that

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Compare the problem in Exercise 54 with that in Exercise 45.

Exercise 45

It is known that for any positive r.v. X, the function n(s) = (E{X^s})^1/s is non-decreasing in s. Prove it, using Jensen’s inequality.

Exercise 54

Which is larger: E{X²} or (E{|X|})²? (Unlike in (3.1.5), we consider |X|.)

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Probability And Stochastic Modeling

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1st Edition

Authors: Vladimir I. Rotar

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Compare the problem in Exercise 54 with that in Exercise 45. Exercise 45 It is known that

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Probability And Stochastic Modeling

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