Displaying similar documents to “On a problem of J. Schnitzer”

A note on optimal probability lower bounds for centered random variables

Mark Veraar (2008)

Colloquium Mathematicae

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We obtain lower bounds for ℙ(ξ ≥ 0) and ℙ(ξ > 0) under assumptions on the moments of a centered random variable ξ. The estimates obtained are shown to be optimal and improve results from the literature. They are then applied to obtain probability lower bounds for second order Rademacher chaos.

On Tchebycheff's type inequalities.

Kosmas Ferentinos (1982)

Trabajos de Estadística e Investigación Operativa

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Three inequalities of Tchebycheff type are presented. Two of them give lower bounds for the probability of intervals not necessarily symmetric around the mean. The third one generalizes the extension of Tchebycheff's inequalities given by Miyamoto (1978). They are based on the inequality of Markov. Attainability of lower bounds is also discussed.