Prove for two random variables X and Y with finite moments, and 1 p Note that Therefore Now, apply Hlder 's inequality X YP X Y P X Y X YP (X Y) X YP X X YP Y ...

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Prove for two random variables X and Y with finite moments, and 1 p Note that

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Prove for two random variables X and Y with finite moments, and 1 ≤ p

Note that |X+YP = |X+Y|P-|X+Y| X+YP (X+Y) X + YP |X| + |X + YP-|Y|.

Therefore

Now, apply Hölder's inequality.

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Introduction To Probability Statistics And Random Processes

ISBN: 9780990637202

1st Edition

Authors: Hossein Pishro-Nik

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Question Posted: Oct 27, 2023 02:30 AM

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Prove for two random variables X and Y with finite moments, and 1 p Note that

Question:

|X+YP = |X+Y|P-¹|X+Y| ≤X+YP ¹ (X+Y) ≤X + YP ¹|X| + |X + YP-¹|Y|.

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Introduction To Probability Statistics And Random Processes

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