Paley–Zygmund inequality
id:
paley-zygmund-inequality-201-13622411
title:
Paley–Zygmund inequality
text:
In mathematics, the Paley–Zygmund inequality bounds the
probability that a positive random variable is small, in terms of
its first two moments. The inequality was
proved by Raymond Paley and Antoni Zygmund. Theorem: If Z ≥ 0 is a random variable with
finite variance, and if 0 ≤ θ ≤ 1 , then Proof: First, The first addend is at most θ E [ Z ] , while the second is at most E [ Z 2 ] 1 / 2 P 1 / 2 by the Cauchy–Schwarz inequality. The desired inequality then follows. ∎
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wiki
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encyclopedia
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original url:
https://en.wikipedia.org/wiki/Paley%E2%80%93Zygmund_inequality
date created:
date modified:
2023-03-12T11:52:47Z
main entity:
{"identifier":"Q2718608","url":"https://www.wikidata.org/entity/Q2718608"}
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