Question: 26. Lyapunovs inequality. Let Z be a positive random variable. By Jensens inequality or otherwise, show that E(Zr )1/r E(Zs )1/s when r

26. Lyapunov’s inequality. Let Z be a positive random variable. By Jensen’s inequality or otherwise, show that E(Zr )1/r ≥ E(Zs )1/s when r ≥ s > 0. Thus, if Z has finite r th moment, then it has finite sth moment, for r ≥ s > 0.

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