(adsbygoogle = window.adsbygoogle || []).push({}); Prove that if X and Y have finite second moments (i.e. E(X^2) and E(Y^2) are finite), then X+Y has a finite second moment.

(X+Y)^2 ≤ X^2 + Y^2 + 2|XY|

=> E[(X+Y)^2] ≤ E(X^2) + E(Y^2) + 2E(|XY|)

I don't understand the (probably incomplete) proof. On the right side, E(X^2) and E(Y^2) are finite, but how can we know whether E(|XY|) is finite or not?

Thanks for explaining!

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# Show that X+Y has a finite second moment

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