Prove for two random variables X and Y with finite moments, and 1 p Note that
Question:
Prove for two random variables X and Y with finite moments, and 1 ≤ p
Note that
Therefore
Now, apply Hölder's inequality.
Transcribed Image Text:
|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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Related Book For
Introduction To Probability Statistics And Random Processes
ISBN: 9780990637202
1st Edition
Authors: Hossein Pishro-Nik
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