Finite sequences representing expected order statistics

Characterizations of finite sequences $β_{1}<\cdots<β_{n}$ representing expected values of order statistics from a random sample of size $n$ are given. As a by-product, a characterization of binomial mixtures, when the mixing random variable is supported in the open interval $(0,1)$, is presented; this enables the exact description of the convex hull of the open binomial curve, as well as the open moment curve.

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