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Let X be a nonnegative random variable Prove that E X E X2 1 2

Let X be a nonnegative random variable.

Prove that

E[X] ≤ (E[X2])1/2 ≤ (E[X3])1/3 ≤ . . .

Prove that

E[X] ≤ (E[X2])1/2 ≤ (E[X3])1/3 ≤ . . .

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