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

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