Paley Zygmund Inequality

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Beschreibung

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Paley Zygmund inequality bounds the probability that a positive random variable is small, in terms of its mean and variance (i.e., 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 1, thenThe right-hand side of the Paley - Zygmund inequality can be written asThe one-sided Chebyshev inequality gives a slightly better bound: