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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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A question about the distributions of order statistics

Let $F_{k:n}(x)$ denote the distribution function of $k$th order statistic, i.e. $k$th lowest of $n$ i.i.d. draws from a smooth distribution $F$ with support $[0,\bar{x}]$. Then $F_{k+1}(x)-F_k(x) \le …
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