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broken link fixed, cf. https://meta.mathoverflow.net/q/5301/70594
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Glorfindel
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Your problem is closely related to order statistics for normal random variables, so you may find this paper useful: Percentage Points and Modes of Order Statistics from the Normal DistributionPercentage Points and Modes of Order Statistics from the Normal Distribution by Shanti S. Gupta

Your problem is closely related to order statistics for normal random variables, so you may find this paper useful: Percentage Points and Modes of Order Statistics from the Normal Distribution by Shanti S. Gupta

Your problem is closely related to order statistics for normal random variables, so you may find this paper useful: Percentage Points and Modes of Order Statistics from the Normal Distribution by Shanti S. Gupta

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John D. Cook
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Your problem is closely related to order statistics for normal random variables, so you may find this paper useful: Percentage Points and Modes of Order Statistics from the Normal Distribution by Shanti S. Gupta