Question: 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)

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{Xs})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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