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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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Gaussian order statistics
Setup. Let $\alpha\in(0,1)$ fixed; and $\tau\in[0,1]$ (think of it very close to one).
Suppose $X_1,\dots,X_n$ are i.i.d. standard normal.
Let $Y_1,\dots,Y_n$ be another sequence of standard normals w …