BRS-inequality

rdf:langString BRS-inequality

rdf:langString BRS-inequality is the short name for Bruss-Robertson-Steele inequality. This inequality gives a convenient upper bound for the expected maximum number of non-negative random variables one can sum up without exceeding a given upper bound . For example, suppose 100 random variables are all uniformly distributed on , not necessarily independent, and let , say. Let be the maximum number of one can select in such that their sum does not exceed . is a random variable, so what can one say about bounds for its expectation? How would an upper bound for behave, if one changes the size of the sample and keeps fixed, or alternatively, if one keeps fixed but varies ? What can one say about , if the uniform distribution is replaced by another continuous distribution? In all generality, what can one say if each may have its own continuous distribution function ?