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Suppose X is a frequency vector that follows a central multiplehyper-geometric distribution, such as arises in random sampling of anm-category attribute from a finite population without replacement. We show thatthe probability that X satisfies some symmetrical, but otherwise arbitrary,interval constraints in each component decreases as the sample size increasesor decreases away from one-half of the population size.

Stochastic Ordering of Symmetric Core Event Probabilities With Respect To Row Margins For Multiple Hypergeometric Random Variables